Rung 34: maintenance of committable units — a fixed, an extendable and a modular committable generator, link and process, each taken off for one event¶
One rung of the PyPSA corpus: the file pypsa.yaml projected onto what this network builds, attached to that network, and held to what PyPSA solves it to.
✔ Verified against pypsa 1.3.0 — objective 6420.048611 on both sides; structure ≠
CVaR0 vs 1 — the file declares the tail's average on every run; PyPSA adds it only under a risk preference, and without one the objective prices it at zero and no row reads it;CVaR-a0 vs 1 — the file declares each scenario's excess on every run; PyPSA adds it only under a risk preference, and without one no row reads it;CVaR-theta0 vs 1 — the file declares the tail's start on every run; PyPSA adds it only under a risk preference, and without one no row reads it; size ✔ 503 rows · ≠ 277 vs 280 columns · ✔ 1153 nonzeros; duals — integer model, no duals; model for model: 131 blocks equal, 0 documented splits, 4 recorded deviations.
Rows and columns, PyPSA against specsolve, name for name
| row | PyPSA | specsolve |
|---|---|---|
Bus-nodal_balance |
12 | 12 |
Generator-com-ext-p-lower |
4 | 4 |
Generator-com-ext-p-lower-nonneg |
4 | 4 |
Generator-com-ext-p-upper-bigM |
4 | 4 |
Generator-com-ext-p-upper-cap |
4 | 4 |
Generator-com-mod-p-lower |
4 | 4 |
Generator-com-mod-p-upper |
4 | 4 |
Generator-com-p-lower |
4 | 4 |
Generator-com-p-upper |
4 | 4 |
Generator-com-transition-shut-down |
12 | 12 |
Generator-com-transition-start-up |
12 | 12 |
Generator-ext-p_nom-lower |
2 | 2 |
Generator-ext-p_nom-upper |
2 | 2 |
Generator-fix-p-lower |
12 | 12 |
Generator-fix-p-upper |
12 | 12 |
Generator-maint-event-count |
3 | 3 |
Generator-maint-modstatus-lb |
4 | 4 |
Generator-maint-modstatus-le-maint |
4 | 4 |
Generator-maint-modstatus-le-status |
4 | 4 |
Generator-maint-start-horizon |
1 | 1 |
Generator-maint-status-lb |
4 | 4 |
Generator-maint-status-le-maint |
4 | 4 |
Generator-maint-status-le-status |
4 | 4 |
Generator-maint-window |
12 | 12 |
Generator-maintcap_lower_nommax |
4 | 4 |
Generator-maintcap_lower_nommin |
4 | 4 |
Generator-maintcap_upper |
4 | 4 |
Generator-maintcap_upper_nommax |
4 | 4 |
Generator-p_nom_modularity |
1 | 1 |
Generator-shut_down-p-fixed-upper |
8 | 8 |
Generator-shut_down-p_nom-variable-upper |
4 | 4 |
Generator-start_up-p-fixed-upper |
8 | 8 |
Generator-start_up-p_nom-variable-upper |
4 | 4 |
Generator-status-p-fixed-upper |
8 | 8 |
Generator-status-p_nom-variable-upper |
4 | 4 |
Link-com-ext-p-lower |
4 | 4 |
Link-com-ext-p-lower-nonneg |
4 | 4 |
Link-com-ext-p-upper-bigM |
4 | 4 |
Link-com-ext-p-upper-cap |
4 | 4 |
Link-com-mod-p-lower |
4 | 4 |
Link-com-mod-p-upper |
4 | 4 |
Link-com-p-lower |
4 | 4 |
Link-com-p-upper |
4 | 4 |
Link-com-transition-shut-down |
12 | 12 |
Link-com-transition-start-up |
12 | 12 |
Link-ext-p_nom-lower |
2 | 2 |
Link-ext-p_nom-upper |
2 | 2 |
Link-fix-p-lower |
4 | 4 |
Link-fix-p-upper |
4 | 4 |
Link-maint-event-count |
3 | 3 |
Link-maint-modstatus-lb |
4 | 4 |
Link-maint-modstatus-le-maint |
4 | 4 |
Link-maint-modstatus-le-status |
4 | 4 |
Link-maint-start-horizon |
1 | 1 |
Link-maint-status-lb |
4 | 4 |
Link-maint-status-le-maint |
4 | 4 |
Link-maint-status-le-status |
4 | 4 |
Link-maint-window |
12 | 12 |
Link-maintcap_lower_nommax |
4 | 4 |
Link-maintcap_lower_nommin |
4 | 4 |
Link-maintcap_upper |
4 | 4 |
Link-maintcap_upper_nommax |
4 | 4 |
Link-p_nom_modularity |
1 | 1 |
Link-shut_down-p-fixed-upper |
8 | 8 |
Link-shut_down-p_nom-variable-upper |
4 | 4 |
Link-start_up-p-fixed-upper |
8 | 8 |
Link-start_up-p_nom-variable-upper |
4 | 4 |
Link-status-p-fixed-upper |
8 | 8 |
Link-status-p_nom-variable-upper |
4 | 4 |
Process-com-ext-p-lower |
4 | 4 |
Process-com-ext-p-lower-nonneg |
4 | 4 |
Process-com-ext-p-upper-bigM |
4 | 4 |
Process-com-ext-p-upper-cap |
4 | 4 |
Process-com-mod-p-lower |
4 | 4 |
Process-com-mod-p-upper |
4 | 4 |
Process-com-p-lower |
4 | 4 |
Process-com-p-upper |
4 | 4 |
Process-com-transition-shut-down |
12 | 12 |
Process-com-transition-start-up |
12 | 12 |
Process-ext-p_nom-lower |
2 | 2 |
Process-ext-p_nom-upper |
2 | 2 |
Process-maint-event-count |
3 | 3 |
Process-maint-modstatus-lb |
4 | 4 |
Process-maint-modstatus-le-maint |
4 | 4 |
Process-maint-modstatus-le-status |
4 | 4 |
Process-maint-start-horizon |
1 | 1 |
Process-maint-status-lb |
4 | 4 |
Process-maint-status-le-maint |
4 | 4 |
Process-maint-status-le-status |
4 | 4 |
Process-maint-window |
12 | 12 |
Process-maintcap_lower_nommax |
4 | 4 |
Process-maintcap_lower_nommin |
4 | 4 |
Process-maintcap_upper |
4 | 4 |
Process-maintcap_upper_nommax |
4 | 4 |
Process-p_nom_modularity |
1 | 1 |
Process-shut_down-p-fixed-upper |
8 | 8 |
Process-shut_down-p_nom-variable-upper |
4 | 4 |
Process-start_up-p-fixed-upper |
8 | 8 |
Process-start_up-p_nom-variable-upper |
4 | 4 |
Process-status-p-fixed-upper |
8 | 8 |
Process-status-p_nom-variable-upper |
4 | 4 |
| column | PyPSA | specsolve |
|---|---|---|
CVaR |
0 | ≠ 1 |
CVaR-a |
0 | ≠ 1 |
CVaR-theta |
0 | ≠ 1 |
Generator-maintenance |
12 | 12 |
Generator-maintenance_capacity |
4 | 4 |
Generator-maintenance_start |
12 | 12 |
Generator-maintenance_status |
8 | 8 |
Generator-n_mod |
1 | 1 |
Generator-p |
24 | 24 |
Generator-p_nom |
2 | 2 |
Generator-shut_down |
12 | 12 |
Generator-start_up |
12 | 12 |
Generator-status |
12 | 12 |
Link-maintenance |
12 | 12 |
Link-maintenance_capacity |
4 | 4 |
Link-maintenance_start |
12 | 12 |
Link-maintenance_status |
8 | 8 |
Link-n_mod |
1 | 1 |
Link-p |
16 | 16 |
Link-p_nom |
2 | 2 |
Link-shut_down |
12 | 12 |
Link-start_up |
12 | 12 |
Link-status |
12 | 12 |
Process-maintenance |
12 | 12 |
Process-maintenance_capacity |
4 | 4 |
Process-maintenance_start |
12 | 12 |
Process-maintenance_status |
8 | 8 |
Process-n_mod |
1 | 1 |
Process-p |
12 | 12 |
Process-p_nom |
2 | 2 |
Process-shut_down |
12 | 12 |
Process-start_up |
12 | 12 |
Process-status |
12 | 12 |
The model¶
The same model, as math
A plain n.optimize(), and its multi-period and stochastic classes, in one file. Every second-stage quantity spans a scenario (a future dispatch is chosen in) and every asset stands in the investment periods its build year and lifetime span. A parameter spans scenario exactly when PyPSA reads it per scenario. Capacity is chosen once, before the future is known, and paid once per active period at its cost in expectation over the scenarios; operation is the expectation over the scenarios' weights, with a share priced at the tail through the CVaR rows, which stand only where that share is positive. A plain run feeds one scenario, one period, all-active masks and unit weights, and the model collapses to the standard one. A security-constrained run copies each branch flow limit once per outage in an outage set that a plain run leaves empty. Which snapshots an asset is active in, a scenario's weight, and the outage factors are data prep.
Sets¶
| Symbol | Meaning |
|---|---|
| \(\Xi\) | index \(\xi\) — scenario with \(\mathrm{Generator\_maintenance\_cover} \subseteq \Xi \times \mathcal{G} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Link\_maintenance\_cover} \subseteq \Xi \times \mathcal{L} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Process\_maintenance\_cover} \subseteq \Xi \times \mathcal{J} \times \mathcal{T} \times \mathcal{T}\) — the futures dispatch is chosen in, each with a weight |
| \(\mathcal{T}\) | index \(t\) — snapshot with \(\mathrm{snapshot\_period}: \mathcal{T} \to \mathcal{Y},\ \mathrm{Generator\_maintenance\_cover} \subseteq \Xi \times \mathcal{G} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Link\_maintenance\_cover} \subseteq \Xi \times \mathcal{L} \times \mathcal{T} \times \mathcal{T},\ \mathrm{Process\_maintenance\_cover} \subseteq \Xi \times \mathcal{J} \times \mathcal{T} \times \mathcal{T}\) — 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 \(\mathrm{Generator\_bus}: \mathcal{G} \to \mathcal{N},\ \mathrm{Generator\_maintenance\_cover} \subseteq \Xi \times \mathcal{G} \times \mathcal{T} \times \mathcal{T}\) — generating units, each on one bus |
| \(\mathcal{L}\) | index \(l\) — link with \(\mathrm{Link\_bus0}: \mathcal{L} \to \mathcal{N},\ \mathrm{Link\_output\_link}: \mathcal{O} \to \mathcal{L},\ \mathrm{Link\_maintenance\_cover} \subseteq \Xi \times \mathcal{L} \times \mathcal{T} \times \mathcal{T}\) — 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 \(\mathrm{Process\_output\_process}: \mathcal{R} \to \mathcal{J},\ \mathrm{Process\_maintenance\_cover} \subseteq \Xi \times \mathcal{J} \times \mathcal{T} \times \mathcal{T}\) — 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 (consistency.py:1187) |
| \(\mathrm{com}\) | Generator_committable over \(\mathcal{G}\) — whether output is gated by an on/off status decision |
| \(\mathrm{u}^{0}\) | Generator_status_initial over \(\Xi \times \mathcal{G}\) — one where the unit was on before the first snapshot, zero where off — PyPSA's up_time_before > 0, data prep |
| \(\mathrm{c}^{\mathrm{up}}\) | Generator_start_up_cost over \(\Xi \times \mathcal{G}\) — cost of one start |
| \(\mathrm{c}^{\mathrm{dn}}\) | Generator_shut_down_cost over \(\Xi \times \mathcal{G}\) — cost of one stop |
| \(\mathrm{c}^{\mathrm{on}}\) | Generator_stand_by_cost over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — cost of one snapshot spent on |
| \(\mathrm{p}^{\mathrm{mod}}\) | Generator_p_nom_mod over \(\mathcal{G}\) — the module size a build comes in whole numbers of; no value means the build is continuous |
| \(\mathrm{N}^{\mathrm{fix}}\) | Generator_modules_installed over \(\Xi \times \mathcal{G}\) — how many whole modules a committable build has in place: Generator_p_nom / Generator_p_nom_mod where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build whose nominal power is not a whole number of modules |
| \(\mathrm{M}\) | Generator_big_m over \(\Xi \times \mathcal{G}\) — a bound safely above any feasible output — the build cap at full availability, data prep |
| \(\mathrm{nonneg}\) | Generator_p_min_pu_nonneg over \(\mathcal{G}\) — true where none of the generator's own minimums-per-unit is negative — PyPSA's per-unit (p_min_pu >= 0).all() over every snapshot and scenario, data prep |
| \(\mathrm{mnt}\) | Generator_maintainable over \(\mathcal{G}\) — whether a generator must be taken off for maintenance within the horizon — in any scenario, as PyPSA takes the union over them (components.py:1016-1019) |
| \(\gamma\) | Generator_maintenance_pu over \(\Xi \times \mathcal{G}\) — the share of the build a maintenance event takes off |
| \(\mathrm{n}^{\mathrm{mnt}}\) | Generator_maintenance_events over \(\Xi \times \mathcal{G}\) — how many maintenance events the horizon holds |
| \(\mathrm{blk}\) | Generator_maintenance_start_blocked over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — true where no maintenance event may start, because the snapshots it would cover run past the end of the horizon or into one the generator does not stand in — PyPSA's active & ~valid, from maintenance_duration and the generator weightings, data prep |
| \(\mathrm{f}^{\mathrm{nom}}\) | Link_p_nom over \(\Xi \times \mathcal{L}\) — nominal power |
| \(\mathrm{ext}^{f}\) | Link_p_nom_extendable over \(\mathcal{L}\) — whether the nominal power is a decision |
| \(\underline{\mathrm{f}}\) | Link_p_min_pu over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — least flow, per unit of nominal power — negative for a link that carries both ways |
| \(\overline{\mathrm{f}}\) | Link_p_max_pu over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — most flow, per unit of nominal power |
| \(\eta\) | Link_efficiency over \(\Xi \times \mathcal{T} \times \mathcal{O}\) — share of the flow that arrives at an output port, PyPSA's efficiency, efficiency2, … read long — negative where that port consumes rather than delivers. Read at the snapshot the flow arrives, so a delayed port delivers at its arrival snapshot's efficiency (constraints.py:1522) |
| \(\mathrm{d}^{f}\) | Link_output_delay over \(\Xi \times \mathcal{O}\) — snapshots a port's delivery lags its link's flow — PyPSA's delay, delay2, … read long, in snapshot_weightings.generators units, which the file states as whole snapshots; zero for a port that delivers at once. Each scenario takes its own. PyPSA 1.3.0 groups the ports by delay over all scenarios and shifts each group in every one, so a delay that differs by scenario delivers the flow twice (constraints.py:1269-1276, PyPSA/PyPSA#1941) |
| \(\mathrm{cyc}^{f}\) | Link_output_cyclic_delay over \(\Xi \times \mathcal{O}\) — 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. Each scenario takes its own, as the delay |
| \(\mathrm{c}^{f}\) | Link_marginal_cost over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — cost of one unit of flow |
| \(\mathrm{c}^{f,(2)}\) | Link_marginal_cost_quadratic over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — cost of the square of one unit of flow |
| \(\mathrm{com}^{f}\) | Link_committable over \(\mathcal{L}\) — whether flow is gated by an on/off status decision |
| \(\mathrm{u}^{f,0}\) | Link_status_initial over \(\Xi \times \mathcal{L}\) — one where the link was on before the first snapshot, zero where off — PyPSA's up_time_before > 0, data prep |
| \(\mathrm{c}^{f,\mathrm{up}}\) | Link_start_up_cost over \(\Xi \times \mathcal{L}\) — cost of one start |
| \(\mathrm{c}^{f,\mathrm{dn}}\) | Link_shut_down_cost over \(\Xi \times \mathcal{L}\) — cost of one stop |
| \(\mathrm{c}^{f,\mathrm{on}}\) | 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 \(\mathcal{L}\) — 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 \(\Xi \times \mathcal{L}\) — a bound safely above any feasible flow — the build cap at full availability, data prep |
| \(\mathrm{nonneg}^{f}\) | Link_p_min_pu_nonneg over \(\mathcal{L}\) — true where none of the link's own minimums-per-unit is negative — PyPSA's per-unit (p_min_pu >= 0).all() over every snapshot and scenario, data prep |
| \(\mathrm{mnt}^{f}\) | Link_maintainable over \(\mathcal{L}\) — whether a link must be taken off for maintenance within the horizon — in any scenario, as PyPSA takes the union over them (components.py:1016-1019) |
| \(\gamma^{f}\) | Link_maintenance_pu over \(\Xi \times \mathcal{L}\) — the share of the build a maintenance event takes off |
| \(\mathrm{n}^{f,\mathrm{mnt}}\) | Link_maintenance_events over \(\Xi \times \mathcal{L}\) — how many maintenance events the horizon holds |
| \(\mathrm{blk}^{f}\) | Link_maintenance_start_blocked over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — true where no maintenance event may start, because the snapshots it would cover run past the end of the horizon or into one the link does not stand in — PyPSA's active & ~valid, from maintenance_duration and the generator weightings, data prep |
| \(\mathrm{z}^{\mathrm{nom}}\) | Process_p_nom over \(\Xi \times \mathcal{J}\) — nominal internal power |
| \(\mathrm{ext}^{z}\) | Process_p_nom_extendable over \(\mathcal{J}\) — whether the nominal internal power is a decision |
| \(\underline{\mathrm{z}}\) | Process_p_min_pu over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — least internal power, per unit of nominal power — negative for a process that runs both ways |
| \(\overline{\mathrm{z}}\) | Process_p_max_pu over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — most internal power, per unit of nominal power |
| \(\alpha\) | Process_rate over \(\Xi \times \mathcal{T} \times \mathcal{R}\) — the energy a port draws or delivers per unit of internal power, PyPSA's rate0, rate1, … read long — negative where the port withdraws, positive where it injects; a link is a process whose bus0 rate is minus one and whose output rates are its efficiencies. Read at the snapshot the transfer arrives, so a delayed port transfers at its arrival snapshot's rate (constraints.py:1522) |
| \(\mathrm{d}^{z}\) | Process_output_delay over \(\Xi \times \mathcal{R}\) — snapshots a port's transfer lags its process's internal power — PyPSA's delay0, delay1, … read long, in snapshot_weightings.generators units, which the file states as whole snapshots; zero for a port that transfers at once. Each scenario takes its own, as a link's |
| \(\mathrm{cyc}^{z}\) | Process_output_cyclic_delay over \(\Xi \times \mathcal{R}\) — 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. Each scenario takes its own, as the delay |
| \(\mathrm{c}^{z}\) | Process_marginal_cost over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — cost of one unit of internal power |
| \(\mathrm{c}^{z,(2)}\) | Process_marginal_cost_quadratic over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — cost of the square of one unit of internal power |
| \(\underline{\mathrm{z}}^{\mathrm{nom}}\) | Process_p_nom_min over \(\Xi \times \mathcal{J}\) — least nominal power an extendable process may be built at |
| \(\overline{\mathrm{z}}^{\mathrm{nom}}\) | Process_p_nom_max over \(\Xi \times \mathcal{J}\) — most nominal power an extendable process may be built at |
| \(\mathrm{c}^{\mathrm{cap},z}\) | Process_capital_cost over \(\Xi \times \mathcal{J}\) — cost of one unit of nominal power — PyPSA's capital_cost, periodized as an annuity in data prep |
| \(\mathrm{com}^{z}\) | Process_committable over \(\mathcal{J}\) — whether internal power is gated by an on/off status decision |
| \(\mathrm{u}^{z,0}\) | Process_status_initial over \(\Xi \times \mathcal{J}\) — one where the process was on before the first snapshot, zero where off — PyPSA's up_time_before > 0, data prep |
| \(\mathrm{c}^{z,\mathrm{up}}\) | Process_start_up_cost over \(\Xi \times \mathcal{J}\) — cost of one start |
| \(\mathrm{c}^{z,\mathrm{dn}}\) | Process_shut_down_cost over \(\Xi \times \mathcal{J}\) — cost of one stop |
| \(\mathrm{c}^{z,\mathrm{on}}\) | 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 \(\mathcal{J}\) — the module size a build comes in whole numbers of; no value means the build is continuous |
| \(\mathrm{N}^{z,\mathrm{fix}}\) | Process_modules_installed over \(\Xi \times \mathcal{J}\) — how many whole modules a committable build has in place: Process_p_nom / Process_p_nom_mod where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build whose nominal power is not a whole number of modules |
| \(\mathrm{M}^{z}\) | Process_big_m over \(\Xi \times \mathcal{J}\) — a bound safely above any feasible internal power — the build cap at full availability, data prep |
| \(\mathrm{nonneg}^{z}\) | Process_p_min_pu_nonneg over \(\mathcal{J}\) — true where none of the process's own minimums-per-unit is negative — PyPSA's per-unit (p_min_pu >= 0).all() over every snapshot and scenario, data prep |
| \(\mathrm{mnt}^{z}\) | Process_maintainable over \(\mathcal{J}\) — whether a process must be taken off for maintenance within the horizon — in any scenario, as PyPSA takes the union over them (components.py:1016-1019) |
| \(\gamma^{z}\) | Process_maintenance_pu over \(\Xi \times \mathcal{J}\) — the share of the build a maintenance event takes off |
| \(\mathrm{n}^{z,\mathrm{mnt}}\) | Process_maintenance_events over \(\Xi \times \mathcal{J}\) — how many maintenance events the horizon holds |
| \(\mathrm{blk}^{z}\) | Process_maintenance_start_blocked over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — true where no maintenance event may start, because the snapshots it would cover run past the end of the horizon or into one the process does not stand in — PyPSA's active & ~valid, from maintenance_duration and the generator weightings, data prep |
| \(\mathrm{load}\) | Load_p_set over \(\Xi \times \mathcal{T} \times \mathcal{D}\) — demand |
| \(\mathrm{sgn}^{\mathrm{load}}\) | Load_sign over \(\mathcal{D}\) — the sign a load's demand enters its bus's balance with — PyPSA's sign, -1 unless given, 1 for a load that feeds its bus. PyPSA refuses one that differs by scenario (consistency.py:1187) |
| \(\mathrm{on}^{\mathrm{load}}\) | 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 (consistency.py:1195) |
| \(\pi\) | scenario_weight over \(\Xi\) — PyPSA's scenario_weightings.weight — the probability of a future |
| \(\omega\) | CVaR_omega (scalar) — PyPSA's risk_preference['omega'] — the share of operating cost priced at the tail rather than in expectation; zero recovers the risk-neutral model |
| \(\mathrm{w}^{y}\) | period_weight_objective over \(\mathcal{Y}\) — PyPSA's investment_period_weightings.objective — what a period's cost weighs |
| \(\mathrm{on}\) | 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 |
| \(\mathrm{W}\) | Generator_capital_weight over \(\mathcal{G}\) — the sum of period weights a generator stands in — PyPSA's active * period_weighting, summed, data prep |
| \(\mathrm{W}^{f}\) | Link_capital_weight over \(\mathcal{L}\) — the sum of period weights a link stands in — PyPSA's active * period_weighting, summed, data prep |
| \(\mathrm{W}^{z}\) | Process_capital_weight over \(\mathcal{J}\) — the sum of period weights a process stands in — PyPSA's active * period_weighting, summed, data prep |
| \(\underline{\mathrm{p}}^{\mathrm{nom}}\) | Generator_p_nom_min over \(\Xi \times \mathcal{G}\) — least nominal power an extendable generator may be built at |
| \(\overline{\mathrm{p}}^{\mathrm{nom}}\) | Generator_p_nom_max over \(\Xi \times \mathcal{G}\) — most nominal power an extendable generator may be built at |
| \(\mathrm{c}^{\mathrm{cap}}\) | Generator_capital_cost over \(\Xi \times \mathcal{G}\) — cost of one unit of nominal power — PyPSA's capital_cost, periodized as an annuity in 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 — PyPSA's capital_cost, periodized as an annuity in data prep |
Variables¶
| Symbol | Meaning |
|---|---|
| \(p\) | Generator_p over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-p — output of a generator in a snapshot |
| \(f\) | Link_p over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-p — PyPSA's p0, the flow measured at the Link_bus0 end: a positive value withdraws there and injects at every bus the link's output ports deliver to |
| \(z\) | Process_p over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-p — PyPSA's internal power p: a positive value drives every port at its own rate, withdrawing where the rate is negative and injecting where it is positive |
| \(N\) | Generator_n_mod over \(\mathcal{G}\) — Generator-n_mod — how many modules of an extendable modular build |
| \(u\) | Generator_status over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-status — how much of a committable unit is on: an integer the rows below cap at one, or at the module count where the build is modular |
| \(\mathit{up}\) | Generator_start_up over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-start_up — how much of a committable unit turns on this snapshot, capped as the status is |
| \(\mathit{dn}\) | Generator_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-shut_down — how much of a committable unit turns off this snapshot, capped as the status is |
| \(\mu\) | Generator_maintenance over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-maintenance — whether a maintainable generator is in maintenance: continuous, and one exactly where an event covers the snapshot |
| \(\mu^{\mathrm{up}}\) | Generator_maintenance_start over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-maintenance_start — whether a maintenance event starts in this snapshot |
| \(\mu^{\mathrm{nom}}\) | Generator_maintenance_capacity over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-maintenance_capacity — the chosen build while in maintenance, zero otherwise: the product the maintcap rows linearize |
| \(\mu^{u}\) | Generator_maintenance_status over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — Generator-maintenance_status — the status while in maintenance, zero otherwise: the product the maint-status rows linearize, so a unit in maintenance may also be off |
| \(N^{f}\) | Link_n_mod over \(\mathcal{L}\) — Link-n_mod — how many modules of an extendable modular build |
| \(u^{f}\) | Link_status over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-status — how much of a committable link is on: an integer the rows below cap at one, or at the module count where the build is modular |
| \(\mathit{up}^{f}\) | Link_start_up over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-start_up — how much of a committable link turns on this snapshot, capped as the status is |
| \(\mathit{dn}^{f}\) | Link_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-shut_down — how much of a committable link turns off this snapshot, capped as the status is |
| \(\mu^{f}\) | Link_maintenance over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-maintenance — whether a maintainable link is in maintenance: continuous, and one exactly where an event covers the snapshot |
| \(\mu^{f,\mathrm{up}}\) | Link_maintenance_start over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-maintenance_start — whether a maintenance event starts in this snapshot |
| \(\mu^{f,\mathrm{nom}}\) | Link_maintenance_capacity over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-maintenance_capacity — the chosen build while in maintenance, zero otherwise: the product the maintcap rows linearize |
| \(\mu^{f,u}\) | Link_maintenance_status over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — Link-maintenance_status — the status while in maintenance, zero otherwise: the product the maint-status rows linearize, so a unit in maintenance may also be off |
| \(N^{z}\) | Process_n_mod over \(\mathcal{J}\) — Process-n_mod — how many modules of an extendable modular build |
| \(u^{z}\) | Process_status over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-status — how much of a committable process is on: an integer the rows below cap at one, or at the module count where the build is modular |
| \(\mathit{up}^{z}\) | Process_start_up over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-start_up — how much of a committable process turns on this snapshot, capped as the status is |
| \(\mathit{dn}^{z}\) | Process_shut_down over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-shut_down — how much of a committable process turns off this snapshot, capped as the status is |
| \(\mu^{z}\) | Process_maintenance over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-maintenance — whether a maintainable process is in maintenance: continuous, and one exactly where an event covers the snapshot |
| \(\mu^{z,\mathrm{up}}\) | Process_maintenance_start over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-maintenance_start — whether a maintenance event starts in this snapshot |
| \(\mu^{z,\mathrm{nom}}\) | Process_maintenance_capacity over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-maintenance_capacity — the chosen build while in maintenance, zero otherwise: the product the maintcap rows linearize |
| \(\mu^{z,u}\) | Process_maintenance_status over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — Process-maintenance_status — the status while in maintenance, zero otherwise: the product the maint-status rows linearize, so a unit in maintenance may also be off |
| \(P\) | Generator_p_nom_ext over \(\mathcal{G}\) — Generator-p_nom — nominal power where it is a decision; the parameter of the same PyPSA name carries the fixed regime |
| \(F\) | Link_p_nom_ext over \(\mathcal{L}\) — Link-p_nom — nominal power where it is a decision; 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; the parameter of the same PyPSA name carries the fixed regime |
| \(a\) | CVaR_a over \(\Xi\) — CVaR-a — how far a scenario's operating cost exceeds the tail's start; nothing where it does not |
| \(\theta\) | CVaR_theta (scalar) — CVaR-theta — where the tail starts, the value at risk |
| \(CVaR\) | CVaR (scalar) — CVaR — the tail's average cost, what the objective prices at omega |
Definitions¶
| Symbol | Meaning |
|---|---|
| \(\mathit{Generator\_previous\_status}\) | Generator_previous_status over \(\Xi \times \mathcal{T} \times \mathcal{G}\) — the commitment state a generator carries into a snapshot — the state it brought into the horizon at the first, the previous snapshot's after that |
| \(\mathit{Link\_previous\_status}\) | Link_previous_status over \(\Xi \times \mathcal{T} \times \mathcal{L}\) — the commitment state a link carries into a snapshot — the state it brought into the horizon at the first, the previous snapshot's after that |
| \(\mathit{Process\_previous\_status}\) | Process_previous_status over \(\Xi \times \mathcal{T} \times \mathcal{J}\) — the commitment state a process carries into a snapshot — the state it brought into the horizon at the first, the previous snapshot's after that |
| \(\mathit{total\_cost}\) | 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 |
| \(\mathit{Bus\_injection}\) | 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 |
| \(\mathit{Generator\_capex}\) | Generator_capex (scalar) |
| \(\mathit{Link\_capex}\) | Link_capex (scalar) |
| \(\mathit{Process\_capex}\) | Process_capex (scalar) |
| \(\mathit{risk\_weighted\_opex}\) | risk_weighted_opex (scalar) |
| \(\mathit{Generator\_injection}\) | Generator_injection over \(\Xi \times \mathcal{T} \times \mathcal{N}\) |
| \(\mathit{Link\_injection}\) | Link_injection over \(\Xi \times \mathcal{T} \times \mathcal{N}\) |
| \(\mathrm{Load\_injection}\) | Load_injection over \(\Xi \times \mathcal{T} \times \mathcal{N}\) |
| \(\mathit{Process\_injection}\) | Process_injection over \(\Xi \times \mathcal{T} \times \mathcal{N}\) |
| \(\mathit{Link\_output\_arrival}\) | 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 |
| \(\mathit{scenario\_opex}\) | 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:414-429) |
| \(\mathrm{Load\_demand}\) | 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:1537-1538) |
| \(\mathit{Generator\_opex}\) | Generator_opex over \(\Xi\) |
| \(\mathit{Generator\_commitment\_opex}\) | Generator_commitment_opex over \(\Xi\) |
| \(\mathit{Link\_opex}\) | Link_opex over \(\Xi\) |
| \(\mathit{Link\_commitment\_opex}\) | Link_commitment_opex over \(\Xi\) |
| \(\mathit{Process\_opex}\) | Process_opex over \(\Xi\) |
| \(\mathit{Process\_commitment\_opex}\) | Process_commitment_opex over \(\Xi\) |
\(t \ominus k\) denotes cyclic translation: index \(t-k\) taken modulo the size of the dimension (roll). Plain \(t-k\) (shift) has no wraparound — terms translated past the edge are simply absent.
\(t \boxminus_{v} k\) denotes translation with \(v\) standing where index \(t-k\) leaves the dimension (shift(edge=v)), so the row at that boundary is built and carries \(v\) rather than being dropped.
\(t \ominus^{\mathrm{relation}(t)} k\) denotes a translation counted inside the group a relation puts \(t\) in (shift(by=relation)), so a term never crosses out of its own group. The two modifiers take different slots — the group above, the fill below — so \(t \boxminus_{v}^{\mathrm{relation}(t)} k\) is both at once.
\(\mathrm{pos}(t)\) denotes where index \(t\) sits along its dimension's own order — the order shift steps along, not the order labels sort in — counted from \(0\). The index itself stays the coordinate, so \(t\) compares against labels and \(\mathrm{pos}(t)\) against positions.
Objective¶
Subject to¶
Generator_fix_p_lower
Generator_fix_p_upper
Link_fix_p_lower
Link_fix_p_upper
Generator_ext_p_nom_lower
Generator_ext_p_nom_upper
Link_ext_p_nom_lower
Link_ext_p_nom_upper
Process_ext_p_nom_lower
Process_ext_p_nom_upper
Generator_com_p_lower
Generator_com_p_upper
Generator_com_transition_start_up
Generator_com_transition_shut_down
Generator_p_nom_modularity
Generator_com_ext_p_upper_cap
Generator_com_ext_p_upper_big_m
Generator_com_ext_p_lower
Generator_com_ext_p_lower_nonneg
Generator_com_mod_p_lower
Generator_com_mod_p_upper
Generator_status_p_fixed_upper
Generator_start_up_p_fixed_upper
Generator_shut_down_p_fixed_upper
Generator_status_p_nom_variable_upper
Generator_start_up_p_nom_variable_upper
Generator_shut_down_p_nom_variable_upper
Generator_maint_event_count
Generator_maint_window
Generator_maint_start_horizon
Generator_maintcap_upper
Generator_maintcap_upper_nommax
Generator_maintcap_lower_nommax
Generator_maintcap_lower_nommin
Generator_maint_status_le_status
Generator_maint_status_le_maint
Generator_maint_status_lb
Generator_maint_modstatus_le_status
Generator_maint_modstatus_le_maint
Generator_maint_modstatus_lb
Link_com_p_lower
Link_com_p_upper
Link_com_transition_start_up
Link_com_transition_shut_down
Link_p_nom_modularity
Link_com_ext_p_upper_cap
Link_com_ext_p_upper_big_m
Link_com_ext_p_lower
Link_com_ext_p_lower_nonneg
Link_com_mod_p_lower
Link_com_mod_p_upper
Link_status_p_fixed_upper
Link_start_up_p_fixed_upper
Link_shut_down_p_fixed_upper
Link_status_p_nom_variable_upper
Link_start_up_p_nom_variable_upper
Link_shut_down_p_nom_variable_upper
Link_maint_event_count
Link_maint_window
Link_maint_start_horizon
Link_maintcap_upper
Link_maintcap_upper_nommax
Link_maintcap_lower_nommax
Link_maintcap_lower_nommin
Link_maint_status_le_status
Link_maint_status_le_maint
Link_maint_status_lb
Link_maint_modstatus_le_status
Link_maint_modstatus_le_maint
Link_maint_modstatus_lb
Process_com_p_lower
Process_com_p_upper
Process_com_transition_start_up
Process_com_transition_shut_down
Process_p_nom_modularity
Process_com_ext_p_upper_cap
Process_com_ext_p_upper_big_m
Process_com_ext_p_lower
Process_com_ext_p_lower_nonneg
Process_com_mod_p_lower
Process_com_mod_p_upper
Process_status_p_fixed_upper
Process_start_up_p_fixed_upper
Process_shut_down_p_fixed_upper
Process_status_p_nom_variable_upper
Process_start_up_p_nom_variable_upper
Process_shut_down_p_nom_variable_upper
Process_maint_event_count
Process_maint_window
Process_maint_start_horizon
Process_maintcap_upper
Process_maintcap_upper_nommax
Process_maintcap_lower_nommax
Process_maintcap_lower_nommin
Process_maint_status_le_status
Process_maint_status_le_maint
Process_maint_status_lb
Process_maint_modstatus_le_status
Process_maint_modstatus_le_maint
Process_maint_modstatus_lb
Bus_nodal_balance
Definitions¶
Generator_previous_status
Link_previous_status
Process_previous_status
total_cost
Bus_injection
Generator_capex
Link_capex
Process_capex
risk_weighted_opex
Generator_injection
Link_injection
Load_injection
Process_injection
Link_output_arrival
Process_output_arrival
scenario_opex
Load_demand
Generator_opex
Generator_commitment_opex
Link_opex
Link_commitment_opex
Process_opex
Process_commitment_opex
Variable domains¶
Generator_p
Link_p
Process_p
Generator_n_mod
Generator_status
Generator_start_up
Generator_shut_down
Generator_maintenance
Generator_maintenance_start
Generator_maintenance_capacity
Generator_maintenance_status
Link_n_mod
Link_status
Link_start_up
Link_shut_down
Link_maintenance
Link_maintenance_start
Link_maintenance_capacity
Link_maintenance_status
Process_n_mod
Process_status
Process_start_up
Process_shut_down
Process_maintenance
Process_maintenance_start
Process_maintenance_capacity
Process_maintenance_status
Generator_p_nom_ext
Link_p_nom_ext
Process_p_nom_ext
CVaR_a
CVaR_theta
CVaR
The spec, differential/pypsa/rungs/rung_34_committable_maintenance.yaml — the file projected onto what this rung builds:
description: A plain `n.optimize()`, and its multi-period and stochastic classes, in one file. Every second-stage
quantity spans a `scenario` (a future dispatch is chosen in) and every asset stands in the investment
`period`s its build year and lifetime span. A parameter spans `scenario` exactly when PyPSA reads it
per scenario. Capacity is chosen once, before the future is known, and paid once per active period at
its cost in expectation over the scenarios; operation is the expectation over the scenarios' weights,
with a share priced at the tail through the CVaR rows, which stand only where that share is positive.
A plain run feeds one scenario, one period, all-active masks and unit weights, and the model collapses
to the standard one. A security-constrained run copies each branch flow limit once per outage in an
`outage` set that a plain run leaves empty. Which snapshots an asset is active in, a scenario's weight,
and the outage factors are data prep.
dimensions:
scenario: {description: 'the futures dispatch is chosen in, each with a weight'}
snapshot: {description: dispatch periods, dtype: datetime}
bus: {description: network nodes}
generator: {description: 'generating units, each on one bus'}
link: {description: 'controllable connections, each from one bus to the buses it delivers to'}
link_output: {description: 'a link''s output ports, one label per port a link declares — PyPSA''s `bus1`,
`bus2`, … columns read long, so a link of any number of output ports is one term in the balance,
data prep'}
process: {description: 'generalized multi-port converters, each with an internal power that every port
draws or delivers at its own rate'}
process_output: {description: 'a process''s ports, one label per port a process declares — PyPSA''s
`bus0`, `bus1`, … each carry a signed `rate`, so a process of any number of ports is one term in
the balance, data prep'}
load: {description: 'demands, each on one bus'}
period: {description: investment periods — PyPSA's `investment_periods`, dtype: int}
relations:
snapshot_period: {description: the investment period a snapshot falls in, key: snapshot, values: period}
Generator_bus: {description: the bus a generator sits on, key: generator, values: bus}
Link_bus0: {description: the bus a link leaves, key: link, values: bus}
Link_output_link: {description: the link an output port belongs to, key: link_output, values: link}
Link_output_bus: {description: 'the bus an output port delivers to — PyPSA''s `bus1`, `bus2`, … columns.
A link of three output ports is three labels here rather than a third relation, so the file states
any number of them', key: link_output, values: bus}
Process_output_process: {description: the process a port belongs to, key: process_output, values: process}
Process_output_bus: {description: 'the bus a port draws from or delivers to — PyPSA''s `bus0`, `bus1`,
… columns. A process of three ports is three labels here rather than a third relation, so the file
states any number of them', key: process_output, values: bus}
Load_bus: {description: the bus a load sits on, key: load, values: bus}
Generator_maintenance_cover:
description: the snapshots a maintenance event covers, by the snapshot it starts in — in a scenario,
the start and the snapshots after it, until their generator weightings reach that scenario's `maintenance_duration`,
data prep; no rows for a generator that is not maintainable
key:
scenario: scenario
generator: generator
start: snapshot
covered: snapshot
Link_maintenance_cover:
description: the snapshots a maintenance event covers, by the snapshot it starts in — in a scenario,
the start and the snapshots after it, until their generator weightings reach that scenario's `maintenance_duration`,
data prep; no rows for a link that is not maintainable
key:
scenario: scenario
link: link
start: snapshot
covered: snapshot
Process_maintenance_cover:
description: the snapshots a maintenance event covers, by the snapshot it starts in — in a scenario,
the start and the snapshots after it, until their generator weightings reach that scenario's `maintenance_duration`,
data prep; no rows for a process that is not maintainable
key:
scenario: scenario
process: process
start: snapshot
covered: snapshot
parameters:
snapshot_weightings_objective:
description: PyPSA's `snapshot_weightings.objective` — hours a snapshot stands for in the cost
dims: [snapshot]
Generator_p_nom:
description: nominal power
dims: [scenario, generator]
Generator_p_nom_extendable:
description: whether the nominal power is a decision
dims: [generator]
dtype: bool
Generator_p_min_pu:
description: least output, per unit of nominal power
dims: [scenario, snapshot, generator]
Generator_p_max_pu:
description: most output, per unit of nominal power — an availability profile
dims: [scenario, snapshot, generator]
Generator_marginal_cost:
description: cost of one unit of output
dims: [scenario, snapshot, generator]
Generator_marginal_cost_quadratic:
description: cost of the square of one unit of output
dims: [scenario, snapshot, generator]
Generator_sign:
description: the sign output enters its bus's balance with — PyPSA's `sign`, `1` unless given, `-1`
for a unit that draws power. PyPSA refuses one that differs by scenario (`consistency.py:1187`)
dims: [generator]
Generator_committable:
description: whether output is gated by an on/off status decision
dims: [generator]
dtype: bool
Generator_status_initial:
description: one where the unit was on before the first snapshot, zero where off — PyPSA's `up_time_before
> 0`, data prep
dims: [scenario, generator]
dtype: int
Generator_start_up_cost:
description: cost of one start
dims: [scenario, generator]
Generator_shut_down_cost:
description: cost of one stop
dims: [scenario, generator]
Generator_stand_by_cost:
description: cost of one snapshot spent on
dims: [scenario, snapshot, generator]
Generator_p_nom_mod:
description: the module size a build comes in whole numbers of; no value means the build is continuous
dims: [generator]
Generator_modules_installed:
description: 'how many whole modules a committable build has in place: `Generator_p_nom / Generator_p_nom_mod`
where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
whose nominal power is not a whole number of modules'
dims: [scenario, generator]
Generator_big_m:
description: a bound safely above any feasible output — the build cap at full availability, data prep
dims: [scenario, generator]
Generator_p_min_pu_nonneg:
description: true where none of the generator's own minimums-per-unit is negative — PyPSA's per-unit
`(p_min_pu >= 0).all()` over every snapshot and scenario, data prep
dims: [generator]
dtype: bool
Generator_maintainable:
description: whether a generator must be taken off for maintenance within the horizon — in any scenario,
as PyPSA takes the union over them (`components.py:1016-1019`)
dims: [generator]
dtype: bool
Generator_maintenance_pu:
description: the share of the build a maintenance event takes off
dims: [scenario, generator]
Generator_maintenance_events:
description: how many maintenance events the horizon holds
dims: [scenario, generator]
dtype: int
Generator_maintenance_start_blocked:
description: true where no maintenance event may start, because the snapshots it would cover run past
the end of the horizon or into one the generator does not stand in — PyPSA's `active & ~valid`,
from `maintenance_duration` and the generator weightings, data prep
dims: [scenario, snapshot, generator]
dtype: bool
Link_p_nom:
description: nominal power
dims: [scenario, link]
Link_p_nom_extendable:
description: whether the nominal power is a decision
dims: [link]
dtype: bool
Link_p_min_pu:
description: least flow, per unit of nominal power — negative for a link that carries both ways
dims: [scenario, snapshot, link]
Link_p_max_pu:
description: most flow, per unit of nominal power
dims: [scenario, snapshot, link]
Link_efficiency:
description: share of the flow that arrives at an output port, PyPSA's `efficiency`, `efficiency2`,
… read long — negative where that port consumes rather than delivers. Read at the snapshot the flow
arrives, so a delayed port delivers at its arrival snapshot's efficiency (`constraints.py:1522`)
dims: [scenario, snapshot, link_output]
Link_output_delay:
description: snapshots a port's delivery lags its link's flow — PyPSA's `delay`, `delay2`, … read
long, in `snapshot_weightings.generators` units, which the file states as whole snapshots; zero
for a port that delivers at once. Each scenario takes its own. PyPSA `1.3.0` groups the ports by
delay over all scenarios and shifts each group in every one, so a delay that differs by scenario
delivers the flow twice (`constraints.py:1269-1276`, PyPSA/PyPSA#1941)
dims: [scenario, link_output]
dtype: int
Link_output_cyclic_delay:
description: whether a delayed port's flow wraps from the end of its investment period — PyPSA's `cyclic_delay`,
`cyclic_delay2`, …; where it does not, the flow still in transit at each period's first snapshots
is lost. Each scenario takes its own, as the delay
dims: [scenario, link_output]
dtype: bool
Link_marginal_cost:
description: cost of one unit of flow
dims: [scenario, snapshot, link]
Link_marginal_cost_quadratic:
description: cost of the square of one unit of flow
dims: [scenario, snapshot, link]
Link_committable:
description: whether flow is gated by an on/off status decision
dims: [link]
dtype: bool
Link_status_initial:
description: one where the link was on before the first snapshot, zero where off — PyPSA's `up_time_before
> 0`, data prep
dims: [scenario, link]
dtype: int
Link_start_up_cost:
description: cost of one start
dims: [scenario, link]
Link_shut_down_cost:
description: cost of one stop
dims: [scenario, link]
Link_stand_by_cost:
description: cost of one snapshot spent on
dims: [scenario, snapshot, link]
Link_p_nom_mod:
description: the module size a build comes in whole numbers of; no value means the build is continuous
dims: [link]
Link_modules_installed:
description: 'how many whole modules a committable build has in place: `Link_p_nom / Link_p_nom_mod`
where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
whose nominal power is not a whole number of modules'
dims: [scenario, link]
Link_big_m:
description: a bound safely above any feasible flow — the build cap at full availability, data prep
dims: [scenario, link]
Link_p_min_pu_nonneg:
description: true where none of the link's own minimums-per-unit is negative — PyPSA's per-unit `(p_min_pu
>= 0).all()` over every snapshot and scenario, data prep
dims: [link]
dtype: bool
Link_maintainable:
description: whether a link must be taken off for maintenance within the horizon — in any scenario,
as PyPSA takes the union over them (`components.py:1016-1019`)
dims: [link]
dtype: bool
Link_maintenance_pu:
description: the share of the build a maintenance event takes off
dims: [scenario, link]
Link_maintenance_events:
description: how many maintenance events the horizon holds
dims: [scenario, link]
dtype: int
Link_maintenance_start_blocked:
description: true where no maintenance event may start, because the snapshots it would cover run past
the end of the horizon or into one the link does not stand in — PyPSA's `active & ~valid`, from
`maintenance_duration` and the generator weightings, data prep
dims: [scenario, snapshot, link]
dtype: bool
Process_p_nom:
description: nominal internal power
dims: [scenario, process]
Process_p_nom_extendable:
description: whether the nominal internal power is a decision
dims: [process]
dtype: bool
Process_p_min_pu:
description: least internal power, per unit of nominal power — negative for a process that runs both
ways
dims: [scenario, snapshot, process]
Process_p_max_pu:
description: most internal power, per unit of nominal power
dims: [scenario, snapshot, process]
Process_rate:
description: the energy a port draws or delivers per unit of internal power, PyPSA's `rate0`, `rate1`,
… read long — negative where the port withdraws, positive where it injects; a link is a process
whose `bus0` rate is minus one and whose output rates are its efficiencies. Read at the snapshot
the transfer arrives, so a delayed port transfers at its arrival snapshot's rate (`constraints.py:1522`)
dims: [scenario, snapshot, process_output]
Process_output_delay:
description: snapshots a port's transfer lags its process's internal power — PyPSA's `delay0`, `delay1`,
… read long, in `snapshot_weightings.generators` units, which the file states as whole snapshots;
zero for a port that transfers at once. Each scenario takes its own, as a link's
dims: [scenario, process_output]
dtype: int
Process_output_cyclic_delay:
description: whether a delayed port's transfer wraps from the end of its investment period — PyPSA's
`cyclic_delay0`, `cyclic_delay1`, …; where it does not, the energy still in transit at each period's
first snapshots is lost. Each scenario takes its own, as the delay
dims: [scenario, process_output]
dtype: bool
Process_marginal_cost:
description: cost of one unit of internal power
dims: [scenario, snapshot, process]
Process_marginal_cost_quadratic:
description: cost of the square of one unit of internal power
dims: [scenario, snapshot, process]
Process_p_nom_min:
description: least nominal power an extendable process may be built at
dims: [scenario, process]
Process_p_nom_max:
description: most nominal power an extendable process may be built at
dims: [scenario, process]
Process_capital_cost:
description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
in data prep
dims: [scenario, process]
Process_committable:
description: whether internal power is gated by an on/off status decision
dims: [process]
dtype: bool
Process_status_initial:
description: one where the process was on before the first snapshot, zero where off — PyPSA's `up_time_before
> 0`, data prep
dims: [scenario, process]
dtype: int
Process_start_up_cost:
description: cost of one start
dims: [scenario, process]
Process_shut_down_cost:
description: cost of one stop
dims: [scenario, process]
Process_stand_by_cost:
description: cost of one snapshot spent on
dims: [scenario, snapshot, process]
Process_p_nom_mod:
description: the module size a build comes in whole numbers of; no value means the build is continuous
dims: [process]
Process_modules_installed:
description: 'how many whole modules a committable build has in place: `Process_p_nom / Process_p_nom_mod`
where a fixed build is modular, one where it is not, data prep. PyPSA refuses a fixed modular build
whose nominal power is not a whole number of modules'
dims: [scenario, process]
Process_big_m:
description: a bound safely above any feasible internal power — the build cap at full availability,
data prep
dims: [scenario, process]
Process_p_min_pu_nonneg:
description: true where none of the process's own minimums-per-unit is negative — PyPSA's per-unit
`(p_min_pu >= 0).all()` over every snapshot and scenario, data prep
dims: [process]
dtype: bool
Process_maintainable:
description: whether a process must be taken off for maintenance within the horizon — in any scenario,
as PyPSA takes the union over them (`components.py:1016-1019`)
dims: [process]
dtype: bool
Process_maintenance_pu:
description: the share of the build a maintenance event takes off
dims: [scenario, process]
Process_maintenance_events:
description: how many maintenance events the horizon holds
dims: [scenario, process]
dtype: int
Process_maintenance_start_blocked:
description: true where no maintenance event may start, because the snapshots it would cover run past
the end of the horizon or into one the process does not stand in — PyPSA's `active & ~valid`, from
`maintenance_duration` and the generator weightings, data prep
dims: [scenario, snapshot, process]
dtype: bool
Load_p_set:
description: demand
dims: [scenario, snapshot, load]
Load_sign:
description: the sign a load's demand enters its bus's balance with — PyPSA's `sign`, `-1` unless
given, `1` for a load that feeds its bus. PyPSA refuses one that differs by scenario (`consistency.py:1187`)
dims: [load]
Load_active:
description: whether a load stands in the model — PyPSA's `active`. A load has no build year and no
lifetime, so the flag holds in every snapshot. PyPSA refuses one that differs by scenario (`consistency.py:1195`)
dims: [load]
dtype: bool
scenario_weight:
description: PyPSA's `scenario_weightings.weight` — the probability of a future
dims: [scenario]
CVaR_omega:
description: PyPSA's `risk_preference['omega']` — the share of operating cost priced at the tail rather
than in expectation; zero recovers the risk-neutral model
dims: []
period_weight_objective:
description: PyPSA's `investment_period_weightings.objective` — what a period's cost weighs
dims: [period]
Generator_active:
description: whether a generator stands in a snapshot's period — PyPSA's `active`, from build year
and lifetime, data prep
dims: [snapshot, generator]
dtype: bool
Link_active:
description: whether a link stands in a snapshot's period — PyPSA's `active`, data prep
dims: [snapshot, link]
dtype: bool
Process_active:
description: whether a process stands in a snapshot's period — PyPSA's `active`, data prep
dims: [snapshot, process]
dtype: bool
Generator_capital_weight:
description: the sum of period weights a generator stands in — PyPSA's `active * period_weighting`,
summed, data prep
dims: [generator]
Link_capital_weight:
description: the sum of period weights a link stands in — PyPSA's `active * period_weighting`, summed,
data prep
dims: [link]
Process_capital_weight:
description: the sum of period weights a process stands in — PyPSA's `active * period_weighting`,
summed, data prep
dims: [process]
Generator_p_nom_min:
description: least nominal power an extendable generator may be built at
dims: [scenario, generator]
Generator_p_nom_max:
description: most nominal power an extendable generator may be built at
dims: [scenario, generator]
Generator_capital_cost:
description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
in data prep
dims: [scenario, generator]
Link_p_nom_min:
description: least nominal power an extendable link may be built at
dims: [scenario, link]
Link_p_nom_max:
description: most nominal power an extendable link may be built at
dims: [scenario, link]
Link_capital_cost:
description: cost of one unit of nominal power — PyPSA's `capital_cost`, periodized as an annuity
in data prep
dims: [scenario, link]
variables:
Generator_p:
description: '`Generator-p` — output of a generator in a snapshot'
dims: [scenario, snapshot, generator]
where: Generator_active
Link_p:
description: '`Link-p` — PyPSA''s `p0`, the flow measured at the `Link_bus0` end: a positive value
withdraws there and injects at every bus the link''s output ports deliver to'
dims: [scenario, snapshot, link]
where: Link_active
Process_p:
description: '`Process-p` — PyPSA''s internal power `p`: a positive value drives every port at its
own rate, withdrawing where the rate is negative and injecting where it is positive'
dims: [scenario, snapshot, process]
where: Process_active
Generator_n_mod:
description: '`Generator-n_mod` — how many modules of an extendable modular build'
dims: [generator]
where: Generator_p_nom_extendable AND Generator_p_nom_mod > 0
domain: integer
bounds: {lower: 0}
Generator_status:
description: '`Generator-status` — how much of a committable unit is on: an integer the rows below
cap at one, or at the module count where the build is modular'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_active
domain: integer
bounds: {lower: 0}
Generator_start_up:
description: '`Generator-start_up` — how much of a committable unit turns on this snapshot, capped
as the status is'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_active
domain: integer
bounds: {lower: 0}
Generator_shut_down:
description: '`Generator-shut_down` — how much of a committable unit turns off this snapshot, capped
as the status is'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_active
domain: integer
bounds: {lower: 0}
Generator_maintenance:
description: '`Generator-maintenance` — whether a maintainable generator is in maintenance: continuous,
and one exactly where an event covers the snapshot'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_active
absence: zero
bounds: {lower: 0, upper: 1}
Generator_maintenance_start:
description: '`Generator-maintenance_start` — whether a maintenance event starts in this snapshot'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_active
absence: zero
domain: binary
Generator_maintenance_capacity:
description: '`Generator-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
the product the `maintcap` rows linearize'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
> 0) AND Generator_active
absence: zero
bounds: {lower: 0}
Generator_maintenance_status:
description: '`Generator-maintenance_status` — the status while in maintenance, zero otherwise: the
product the `maint-status` rows linearize, so a unit in maintenance may also be off'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_committable AND NOT (Generator_p_nom_extendable AND NOT
(Generator_p_nom_mod > 0)) AND Generator_active
absence: zero
bounds: {lower: 0}
Link_n_mod:
description: '`Link-n_mod` — how many modules of an extendable modular build'
dims: [link]
where: Link_p_nom_extendable AND Link_p_nom_mod > 0
domain: integer
bounds: {lower: 0}
Link_status:
description: '`Link-status` — how much of a committable link is on: an integer the rows below cap
at one, or at the module count where the build is modular'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_active
domain: integer
bounds: {lower: 0}
Link_start_up:
description: '`Link-start_up` — how much of a committable link turns on this snapshot, capped as the
status is'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_active
domain: integer
bounds: {lower: 0}
Link_shut_down:
description: '`Link-shut_down` — how much of a committable link turns off this snapshot, capped as
the status is'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_active
domain: integer
bounds: {lower: 0}
Link_maintenance:
description: '`Link-maintenance` — whether a maintainable link is in maintenance: continuous, and
one exactly where an event covers the snapshot'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_active
absence: zero
bounds: {lower: 0, upper: 1}
Link_maintenance_start:
description: '`Link-maintenance_start` — whether a maintenance event starts in this snapshot'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_active
absence: zero
domain: binary
Link_maintenance_capacity:
description: '`Link-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
the product the `maintcap` rows linearize'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
0) AND Link_active
absence: zero
bounds: {lower: 0}
Link_maintenance_status:
description: '`Link-maintenance_status` — the status while in maintenance, zero otherwise: the product
the `maint-status` rows linearize, so a unit in maintenance may also be off'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_committable AND NOT (Link_p_nom_extendable AND NOT (Link_p_nom_mod
> 0)) AND Link_active
absence: zero
bounds: {lower: 0}
Process_n_mod:
description: '`Process-n_mod` — how many modules of an extendable modular build'
dims: [process]
where: Process_p_nom_extendable AND Process_p_nom_mod > 0
domain: integer
bounds: {lower: 0}
Process_status:
description: '`Process-status` — how much of a committable process is on: an integer the rows below
cap at one, or at the module count where the build is modular'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_active
domain: integer
bounds: {lower: 0}
Process_start_up:
description: '`Process-start_up` — how much of a committable process turns on this snapshot, capped
as the status is'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_active
domain: integer
bounds: {lower: 0}
Process_shut_down:
description: '`Process-shut_down` — how much of a committable process turns off this snapshot, capped
as the status is'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_active
domain: integer
bounds: {lower: 0}
Process_maintenance:
description: '`Process-maintenance` — whether a maintainable process is in maintenance: continuous,
and one exactly where an event covers the snapshot'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_active
absence: zero
bounds: {lower: 0, upper: 1}
Process_maintenance_start:
description: '`Process-maintenance_start` — whether a maintenance event starts in this snapshot'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_active
absence: zero
domain: binary
Process_maintenance_capacity:
description: '`Process-maintenance_capacity` — the chosen build while in maintenance, zero otherwise:
the product the `maintcap` rows linearize'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
> 0) AND Process_active
absence: zero
bounds: {lower: 0}
Process_maintenance_status:
description: '`Process-maintenance_status` — the status while in maintenance, zero otherwise: the
product the `maint-status` rows linearize, so a unit in maintenance may also be off'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_committable AND NOT (Process_p_nom_extendable AND NOT (Process_p_nom_mod
> 0)) AND Process_active
absence: zero
bounds: {lower: 0}
Generator_p_nom_ext:
description: '`Generator-p_nom` — nominal power where it is a decision; the parameter of the same
PyPSA name carries the fixed regime'
dims: [generator]
where: Generator_p_nom_extendable
Link_p_nom_ext:
description: '`Link-p_nom` — nominal power where it is a decision; the parameter of the same PyPSA
name carries the fixed regime'
dims: [link]
where: Link_p_nom_extendable
Process_p_nom_ext:
description: '`Process-p_nom` — nominal internal power where it is a decision; the parameter of the
same PyPSA name carries the fixed regime'
dims: [process]
where: Process_p_nom_extendable
CVaR_a:
description: '`CVaR-a` — how far a scenario''s operating cost exceeds the tail''s start; nothing where
it does not'
dims: [scenario]
bounds: {lower: 0}
CVaR_theta:
description: '`CVaR-theta` — where the tail starts, the value at risk'
dims: []
CVaR:
description: '`CVaR` — the tail''s average cost, what the objective prices at `omega`'
dims: []
constraints:
Generator_fix_p_lower:
description: '`Generator-fix-p-lower` — a fixed generator outputs at least its minimum'
dims: [scenario, snapshot, generator]
where: not Generator_p_nom_extendable AND not Generator_committable AND Generator_active
expression: Generator_p >= Generator_p_min_pu * Generator_p_nom * (1 - Generator_maintenance_pu *
Generator_maintenance)
Generator_fix_p_upper:
description: '`Generator-fix-p-upper` — a fixed generator outputs at most what is available'
dims: [scenario, snapshot, generator]
where: not Generator_p_nom_extendable AND not Generator_committable AND Generator_active
expression: Generator_p <= Generator_p_max_pu * Generator_p_nom * (1 - Generator_maintenance_pu *
Generator_maintenance)
Link_fix_p_lower:
description: '`Link-fix-p-lower` — a fixed link carries at least its minimum, negative for the other
way'
dims: [scenario, snapshot, link]
where: not Link_p_nom_extendable AND not Link_committable AND Link_active
expression: Link_p >= Link_p_min_pu * Link_p_nom * (1 - Link_maintenance_pu * Link_maintenance)
Link_fix_p_upper:
description: '`Link-fix-p-upper` — a fixed link carries at most its nominal power'
dims: [scenario, snapshot, link]
where: not Link_p_nom_extendable AND not Link_committable AND Link_active
expression: Link_p <= Link_p_max_pu * Link_p_nom * (1 - Link_maintenance_pu * Link_maintenance)
Generator_ext_p_nom_lower:
description: '`Generator-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
dims: [scenario, generator]
where: Generator_p_nom_extendable
expression: Generator_p_nom_ext >= Generator_p_nom_min
Generator_ext_p_nom_upper:
description: '`Generator-ext-p_nom-upper` — the chosen build is at most its cap in every scenario;
a cap of infinity is no row'
dims: [scenario, generator]
where: Generator_p_nom_extendable AND Generator_p_nom_max
expression: Generator_p_nom_ext <= Generator_p_nom_max
Link_ext_p_nom_lower:
description: '`Link-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
dims: [scenario, link]
where: Link_p_nom_extendable
expression: Link_p_nom_ext >= Link_p_nom_min
Link_ext_p_nom_upper:
description: '`Link-ext-p_nom-upper` — the chosen build is at most its cap in every scenario; a cap
of infinity is no row'
dims: [scenario, link]
where: Link_p_nom_extendable AND Link_p_nom_max
expression: Link_p_nom_ext <= Link_p_nom_max
Process_ext_p_nom_lower:
description: '`Process-ext-p_nom-lower` — the chosen build is at least its floor in every scenario'
dims: [scenario, process]
where: Process_p_nom_extendable
expression: Process_p_nom_ext >= Process_p_nom_min
Process_ext_p_nom_upper:
description: '`Process-ext-p_nom-upper` — the chosen build is at most its cap in every scenario; a
cap of infinity is no row'
dims: [scenario, process]
where: Process_p_nom_extendable AND Process_p_nom_max
expression: Process_p_nom_ext <= Process_p_nom_max
Generator_com_p_lower:
description: '`Generator-com-p-lower` — a committed unit outputs at least its minimum; off, at least
nothing'
dims: [scenario, snapshot, generator]
where: Generator_committable AND not Generator_p_nom_extendable AND Generator_active
expression: Generator_p >= Generator_p_min_pu * Generator_p_nom * (Generator_status - Generator_maintenance_pu
* Generator_maintenance_status)
Generator_com_p_upper:
description: '`Generator-com-p-upper` — a committed unit outputs at most what is available; off, at
most nothing'
dims: [scenario, snapshot, generator]
where: Generator_committable AND not Generator_p_nom_extendable AND Generator_active
expression: Generator_p <= Generator_p_max_pu * Generator_p_nom * (Generator_status - Generator_maintenance_pu
* Generator_maintenance_status)
Generator_com_transition_start_up:
description: '`Generator-com-transition-start-up` — turning on is a start, counted against the state
the unit carried into the snapshot'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_active
expression: Generator_start_up >= Generator_status - Generator_previous_status
Generator_com_transition_shut_down:
description: '`Generator-com-transition-shut-down` — turning off is a stop, counted against the state
the unit carried into the snapshot'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_active
expression: Generator_shut_down >= Generator_previous_status - Generator_status
Generator_p_nom_modularity:
description: '`Generator-p_nom_modularity` — the chosen build is a whole number of modules'
dims: [generator]
where: Generator_p_nom_extendable AND Generator_p_nom_mod > 0
expression: Generator_p_nom_ext == Generator_p_nom_mod * Generator_n_mod
Generator_com_ext_p_upper_cap:
description: '`Generator-com-ext-p-upper-cap` — a committed extendable unit outputs at most what is
available of the chosen build, whatever its status'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0) AND
Generator_active
expression: Generator_p <= Generator_p_max_pu * (Generator_p_nom_ext - Generator_maintenance_pu *
Generator_maintenance_capacity)
Generator_com_ext_p_upper_big_m:
description: '`Generator-com-ext-p-upper-bigM` — off, a unit outputs nothing; on, the big M is no
bound'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0) AND
Generator_active
expression: Generator_p <= Generator_big_m * Generator_status
Generator_com_ext_p_lower:
description: '`Generator-com-ext-p-lower` — a committed extendable unit outputs at least its minimum
of the chosen build; off, the big M releases the row'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_extendable AND NOT (Generator_p_nom_mod > 0) AND
Generator_active
expression: Generator_p >= Generator_p_min_pu * (Generator_p_nom_ext - Generator_maintenance_pu *
Generator_maintenance_capacity) + Generator_big_m * Generator_status - Generator_big_m
Generator_com_ext_p_lower_nonneg:
description: '`Generator-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, output is
also plainly non-negative, a row the big-M lower cannot assert while the unit is off'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_min_pu_nonneg AND NOT
(Generator_p_nom_mod > 0) AND Generator_active
expression: Generator_p >= 0
Generator_com_mod_p_lower:
description: '`Generator-com-mod-p-lower` — a committed modular unit outputs at least its minimum
of one module, whether the build is fixed or a decision'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_p >= Generator_p_min_pu * Generator_p_nom_mod * (Generator_status - Generator_maintenance_pu
* Generator_maintenance_status)
Generator_com_mod_p_upper:
description: '`Generator-com-mod-p-upper` — a committed modular unit outputs at most one module''s
share, whether the build is fixed or a decision'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_p <= Generator_p_max_pu * Generator_p_nom_mod * (Generator_status - Generator_maintenance_pu
* Generator_maintenance_status)
Generator_status_p_fixed_upper:
description: '`Generator-status-p-fixed-upper` — a status is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, generator]
where: Generator_committable AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0) AND
Generator_active
expression: Generator_status <= Generator_modules_installed
Generator_start_up_p_fixed_upper:
description: '`Generator-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, generator]
where: Generator_committable AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0) AND
Generator_active
expression: Generator_start_up <= Generator_modules_installed
Generator_shut_down_p_fixed_upper:
description: '`Generator-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, generator]
where: Generator_committable AND NOT (Generator_p_nom_extendable AND Generator_p_nom_mod > 0) AND
Generator_active
expression: Generator_shut_down <= Generator_modules_installed
Generator_status_p_nom_variable_upper:
description: '`Generator-status-p_nom-variable-upper` — a modular unit is on only where a module is
built'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_status <= Generator_n_mod
Generator_start_up_p_nom_variable_upper:
description: '`Generator-start_up-p_nom-variable-upper` — a modular unit starts only where a module
is built'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_start_up <= Generator_n_mod
Generator_shut_down_p_nom_variable_upper:
description: '`Generator-shut_down-p_nom-variable-upper` — a modular unit stops only where a module
is built'
dims: [scenario, snapshot, generator]
where: Generator_committable AND Generator_p_nom_extendable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_shut_down <= Generator_n_mod
Generator_maint_event_count:
description: '`Generator-maint-event-count` — a maintainable generator holds its number of maintenance
events over the horizon'
dims: [scenario, generator]
where: Generator_maintainable
expression: sum(Generator_maintenance_start, over=snapshot) == Generator_maintenance_events
Generator_maint_window:
description: '`Generator-maint-window` — a generator is in maintenance exactly where an event it started
covers the snapshot; two events do not overlap, since the maintenance status is at most one'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_active
expression: Generator_maintenance == sum(Generator_maintenance_start, by=Generator_maintenance_cover,
over=start, into=covered)
Generator_maint_start_horizon:
description: '`Generator-maint-start-horizon` — no event starts where it could not run its whole duration'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_active AND Generator_maintenance_start_blocked
expression: Generator_maintenance_start == 0
Generator_maintcap_upper:
description: '`Generator-maintcap_upper` — the build taken off is at most the chosen build in maintenance,
and at most the build less its floor out of it'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
> 0) AND Generator_active
expression: Generator_maintenance_capacity <= Generator_p_nom_ext - Generator_p_nom_min * (1 - Generator_maintenance)
Generator_maintcap_upper_nommax:
description: '`Generator-maintcap_upper_nommax` — out of maintenance, no build is taken off'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
> 0) AND Generator_active
expression: Generator_maintenance_capacity <= Generator_p_nom_max * Generator_maintenance
Generator_maintcap_lower_nommax:
description: '`Generator-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken
off'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
> 0) AND Generator_active
expression: Generator_maintenance_capacity >= Generator_p_nom_ext - Generator_p_nom_max * (1 - Generator_maintenance)
Generator_maintcap_lower_nommin:
description: '`Generator-maintcap_lower_nommin` — in maintenance, at least the floor of the build
is taken off'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_p_nom_extendable AND NOT (Generator_committable AND Generator_p_nom_mod
> 0) AND Generator_active AND Generator_p_nom_min > 0
expression: Generator_maintenance_capacity >= Generator_p_nom_min * Generator_maintenance
Generator_maint_status_le_status:
description: '`Generator-maint-status-le-status` — the status in maintenance is at most the status'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_committable AND NOT Generator_p_nom_extendable AND Generator_active
expression: Generator_maintenance_status <= Generator_status
Generator_maint_status_le_maint:
description: '`Generator-maint-status-le-maint` — out of maintenance, the status in maintenance is
zero'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_committable AND NOT Generator_p_nom_extendable AND Generator_active
expression: Generator_maintenance_status <= Generator_maintenance
Generator_maint_status_lb:
description: '`Generator-maint-status-lb` — on and in maintenance, the status in maintenance is one'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_committable AND NOT Generator_p_nom_extendable AND Generator_active
expression: Generator_maintenance_status >= Generator_status + Generator_maintenance - 1
Generator_maint_modstatus_le_status:
description: '`Generator-maint-modstatus-le-status` — the modules on in maintenance are at most the
modules on'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_maintenance_status <= Generator_status
Generator_maint_modstatus_le_maint:
description: '`Generator-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
in it, at most the modules the build cap holds'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_maintenance_status <= Generator_p_nom_max / Generator_p_nom_mod * Generator_maintenance
Generator_maint_modstatus_lb:
description: '`Generator-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
dims: [scenario, snapshot, generator]
where: Generator_maintainable AND Generator_committable AND Generator_p_nom_mod > 0 AND Generator_active
expression: Generator_maintenance_status >= Generator_status - Generator_p_nom_max / Generator_p_nom_mod
* (1 - Generator_maintenance)
Link_com_p_lower:
description: '`Link-com-p-lower` — a committed link flows at least its minimum; off, at least nothing'
dims: [scenario, snapshot, link]
where: Link_committable AND not Link_p_nom_extendable AND Link_active
expression: Link_p >= Link_p_min_pu * Link_p_nom * (Link_status - Link_maintenance_pu * Link_maintenance_status)
Link_com_p_upper:
description: '`Link-com-p-upper` — a committed link flows at most what is available; off, at most
nothing'
dims: [scenario, snapshot, link]
where: Link_committable AND not Link_p_nom_extendable AND Link_active
expression: Link_p <= Link_p_max_pu * Link_p_nom * (Link_status - Link_maintenance_pu * Link_maintenance_status)
Link_com_transition_start_up:
description: '`Link-com-transition-start-up` — turning on is a start, counted against the state the
link carried into the snapshot'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_active
expression: Link_start_up >= Link_status - Link_previous_status
Link_com_transition_shut_down:
description: '`Link-com-transition-shut-down` — turning off is a stop, counted against the state the
link carried into the snapshot'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_active
expression: Link_shut_down >= Link_previous_status - Link_status
Link_p_nom_modularity:
description: '`Link-p_nom_modularity` — the chosen build is a whole number of modules'
dims: [link]
where: Link_p_nom_extendable AND Link_p_nom_mod > 0
expression: Link_p_nom_ext == Link_p_nom_mod * Link_n_mod
Link_com_ext_p_upper_cap:
description: '`Link-com-ext-p-upper-cap` — a committed extendable link flows at most what is available
of the chosen build, whatever its status'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND Link_active
expression: Link_p <= Link_p_max_pu * (Link_p_nom_ext - Link_maintenance_pu * Link_maintenance_capacity)
Link_com_ext_p_upper_big_m:
description: '`Link-com-ext-p-upper-bigM` — off, a link flows nothing; on, the big M is no bound'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND Link_active
expression: Link_p <= Link_big_m * Link_status
Link_com_ext_p_lower:
description: '`Link-com-ext-p-lower` — a committed extendable link flows at least its minimum of the
chosen build; off, the big M releases the row'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_extendable AND NOT (Link_p_nom_mod > 0) AND Link_active
expression: Link_p >= Link_p_min_pu * (Link_p_nom_ext - Link_maintenance_pu * Link_maintenance_capacity)
+ Link_big_m * Link_status - Link_big_m
Link_com_ext_p_lower_nonneg:
description: '`Link-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, flow is also
plainly non-negative, a row the big-M lower cannot assert while the link is off'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_extendable AND Link_p_min_pu_nonneg AND NOT (Link_p_nom_mod
> 0) AND Link_active
expression: Link_p >= 0
Link_com_mod_p_lower:
description: '`Link-com-mod-p-lower` — a committed modular link flows at least its minimum of one
module, whether the build is fixed or a decision'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_p >= Link_p_min_pu * Link_p_nom_mod * (Link_status - Link_maintenance_pu * Link_maintenance_status)
Link_com_mod_p_upper:
description: '`Link-com-mod-p-upper` — a committed modular link flows at most one module''s share,
whether the build is fixed or a decision'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_p <= Link_p_max_pu * Link_p_nom_mod * (Link_status - Link_maintenance_pu * Link_maintenance_status)
Link_status_p_fixed_upper:
description: '`Link-status-p-fixed-upper` — a status is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, link]
where: Link_committable AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0) AND Link_active
expression: Link_status <= Link_modules_installed
Link_start_up_p_fixed_upper:
description: '`Link-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, link]
where: Link_committable AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0) AND Link_active
expression: Link_start_up <= Link_modules_installed
Link_shut_down_p_fixed_upper:
description: '`Link-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, link]
where: Link_committable AND NOT (Link_p_nom_extendable AND Link_p_nom_mod > 0) AND Link_active
expression: Link_shut_down <= Link_modules_installed
Link_status_p_nom_variable_upper:
description: '`Link-status-p_nom-variable-upper` — a modular link is on only where a module is built'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_status <= Link_n_mod
Link_start_up_p_nom_variable_upper:
description: '`Link-start_up-p_nom-variable-upper` — a modular link starts only where a module is
built'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_start_up <= Link_n_mod
Link_shut_down_p_nom_variable_upper:
description: '`Link-shut_down-p_nom-variable-upper` — a modular link stops only where a module is
built'
dims: [scenario, snapshot, link]
where: Link_committable AND Link_p_nom_extendable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_shut_down <= Link_n_mod
Link_maint_event_count:
description: '`Link-maint-event-count` — a maintainable link holds its number of maintenance events
over the horizon'
dims: [scenario, link]
where: Link_maintainable
expression: sum(Link_maintenance_start, over=snapshot) == Link_maintenance_events
Link_maint_window:
description: '`Link-maint-window` — a link is in maintenance exactly where an event it started covers
the snapshot; two events do not overlap, since the maintenance status is at most one'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_active
expression: Link_maintenance == sum(Link_maintenance_start, by=Link_maintenance_cover, over=start,
into=covered)
Link_maint_start_horizon:
description: '`Link-maint-start-horizon` — no event starts where it could not run its whole duration'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_active AND Link_maintenance_start_blocked
expression: Link_maintenance_start == 0
Link_maintcap_upper:
description: '`Link-maintcap_upper` — the build taken off is at most the chosen build in maintenance,
and at most the build less its floor out of it'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
0) AND Link_active
expression: Link_maintenance_capacity <= Link_p_nom_ext - Link_p_nom_min * (1 - Link_maintenance)
Link_maintcap_upper_nommax:
description: '`Link-maintcap_upper_nommax` — out of maintenance, no build is taken off'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
0) AND Link_active
expression: Link_maintenance_capacity <= Link_p_nom_max * Link_maintenance
Link_maintcap_lower_nommax:
description: '`Link-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken off'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
0) AND Link_active
expression: Link_maintenance_capacity >= Link_p_nom_ext - Link_p_nom_max * (1 - Link_maintenance)
Link_maintcap_lower_nommin:
description: '`Link-maintcap_lower_nommin` — in maintenance, at least the floor of the build is taken
off'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_p_nom_extendable AND NOT (Link_committable AND Link_p_nom_mod >
0) AND Link_active AND Link_p_nom_min > 0
expression: Link_maintenance_capacity >= Link_p_nom_min * Link_maintenance
Link_maint_status_le_status:
description: '`Link-maint-status-le-status` — the status in maintenance is at most the status'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_committable AND NOT Link_p_nom_extendable AND Link_active
expression: Link_maintenance_status <= Link_status
Link_maint_status_le_maint:
description: '`Link-maint-status-le-maint` — out of maintenance, the status in maintenance is zero'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_committable AND NOT Link_p_nom_extendable AND Link_active
expression: Link_maintenance_status <= Link_maintenance
Link_maint_status_lb:
description: '`Link-maint-status-lb` — on and in maintenance, the status in maintenance is one'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_committable AND NOT Link_p_nom_extendable AND Link_active
expression: Link_maintenance_status >= Link_status + Link_maintenance - 1
Link_maint_modstatus_le_status:
description: '`Link-maint-modstatus-le-status` — the modules on in maintenance are at most the modules
on'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_committable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_maintenance_status <= Link_status
Link_maint_modstatus_le_maint:
description: '`Link-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
in it, at most the modules the build cap holds'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_committable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_maintenance_status <= Link_p_nom_max / Link_p_nom_mod * Link_maintenance
Link_maint_modstatus_lb:
description: '`Link-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
dims: [scenario, snapshot, link]
where: Link_maintainable AND Link_committable AND Link_p_nom_mod > 0 AND Link_active
expression: Link_maintenance_status >= Link_status - Link_p_nom_max / Link_p_nom_mod * (1 - Link_maintenance)
Process_com_p_lower:
description: '`Process-com-p-lower` — a committed process runs at least its minimum; off, at least
nothing'
dims: [scenario, snapshot, process]
where: Process_committable AND not Process_p_nom_extendable AND Process_active
expression: Process_p >= Process_p_min_pu * Process_p_nom * (Process_status - Process_maintenance_pu
* Process_maintenance_status)
Process_com_p_upper:
description: '`Process-com-p-upper` — a committed process runs at most what is available; off, at
most nothing'
dims: [scenario, snapshot, process]
where: Process_committable AND not Process_p_nom_extendable AND Process_active
expression: Process_p <= Process_p_max_pu * Process_p_nom * (Process_status - Process_maintenance_pu
* Process_maintenance_status)
Process_com_transition_start_up:
description: '`Process-com-transition-start-up` — turning on is a start, counted against the state
the process carried into the snapshot'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_active
expression: Process_start_up >= Process_status - Process_previous_status
Process_com_transition_shut_down:
description: '`Process-com-transition-shut-down` — turning off is a stop, counted against the state
the process carried into the snapshot'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_active
expression: Process_shut_down >= Process_previous_status - Process_status
Process_p_nom_modularity:
description: '`Process-p_nom_modularity` — the chosen build is a whole number of modules'
dims: [process]
where: Process_p_nom_extendable AND Process_p_nom_mod > 0
expression: Process_p_nom_ext == Process_p_nom_mod * Process_n_mod
Process_com_ext_p_upper_cap:
description: '`Process-com-ext-p-upper-cap` — a committed extendable process runs at most what is
available of the chosen build, whatever its status'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0) AND Process_active
expression: Process_p <= Process_p_max_pu * (Process_p_nom_ext - Process_maintenance_pu * Process_maintenance_capacity)
Process_com_ext_p_upper_big_m:
description: '`Process-com-ext-p-upper-bigM` — off, a process does not run; on, the big M is no bound'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0) AND Process_active
expression: Process_p <= Process_big_m * Process_status
Process_com_ext_p_lower:
description: '`Process-com-ext-p-lower` — a committed extendable process runs at least its minimum
of the chosen build; off, the big M releases the row'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_extendable AND NOT (Process_p_nom_mod > 0) AND Process_active
expression: Process_p >= Process_p_min_pu * (Process_p_nom_ext - Process_maintenance_pu * Process_maintenance_capacity)
+ Process_big_m * Process_status - Process_big_m
Process_com_ext_p_lower_nonneg:
description: '`Process-com-ext-p-lower-nonneg` — where no minimum-per-unit is negative, internal power
is also plainly non-negative, a row the big-M lower cannot assert while the process is off'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_extendable AND Process_p_min_pu_nonneg AND NOT (Process_p_nom_mod
> 0) AND Process_active
expression: Process_p >= 0
Process_com_mod_p_lower:
description: '`Process-com-mod-p-lower` — a committed modular process runs at least its minimum of
one module, whether the build is fixed or a decision'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_p >= Process_p_min_pu * Process_p_nom_mod * (Process_status - Process_maintenance_pu
* Process_maintenance_status)
Process_com_mod_p_upper:
description: '`Process-com-mod-p-upper` — a committed modular process runs at most one module''s share,
whether the build is fixed or a decision'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_p <= Process_p_max_pu * Process_p_nom_mod * (Process_status - Process_maintenance_pu
* Process_maintenance_status)
Process_status_p_fixed_upper:
description: '`Process-status-p-fixed-upper` — a status is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, process]
where: Process_committable AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0) AND Process_active
expression: Process_status <= Process_modules_installed
Process_start_up_p_fixed_upper:
description: '`Process-start_up-p-fixed-upper` — a start is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, process]
where: Process_committable AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0) AND Process_active
expression: Process_start_up <= Process_modules_installed
Process_shut_down_p_fixed_upper:
description: '`Process-shut_down-p-fixed-upper` — a stop is at most the modules in place, an explicit
row as PyPSA writes it: one where the build is not modular, and the fixed build''s whole count of
modules where it is'
dims: [scenario, snapshot, process]
where: Process_committable AND NOT (Process_p_nom_extendable AND Process_p_nom_mod > 0) AND Process_active
expression: Process_shut_down <= Process_modules_installed
Process_status_p_nom_variable_upper:
description: '`Process-status-p_nom-variable-upper` — a modular process is on only where a module
is built'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_status <= Process_n_mod
Process_start_up_p_nom_variable_upper:
description: '`Process-start_up-p_nom-variable-upper` — a modular process starts only where a module
is built'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_start_up <= Process_n_mod
Process_shut_down_p_nom_variable_upper:
description: '`Process-shut_down-p_nom-variable-upper` — a modular process stops only where a module
is built'
dims: [scenario, snapshot, process]
where: Process_committable AND Process_p_nom_extendable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_shut_down <= Process_n_mod
Process_maint_event_count:
description: '`Process-maint-event-count` — a maintainable process holds its number of maintenance
events over the horizon'
dims: [scenario, process]
where: Process_maintainable
expression: sum(Process_maintenance_start, over=snapshot) == Process_maintenance_events
Process_maint_window:
description: '`Process-maint-window` — a process is in maintenance exactly where an event it started
covers the snapshot; two events do not overlap, since the maintenance status is at most one'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_active
expression: Process_maintenance == sum(Process_maintenance_start, by=Process_maintenance_cover, over=start,
into=covered)
Process_maint_start_horizon:
description: '`Process-maint-start-horizon` — no event starts where it could not run its whole duration'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_active AND Process_maintenance_start_blocked
expression: Process_maintenance_start == 0
Process_maintcap_upper:
description: '`Process-maintcap_upper` — the build taken off is at most the chosen build in maintenance,
and at most the build less its floor out of it'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
> 0) AND Process_active
expression: Process_maintenance_capacity <= Process_p_nom_ext - Process_p_nom_min * (1 - Process_maintenance)
Process_maintcap_upper_nommax:
description: '`Process-maintcap_upper_nommax` — out of maintenance, no build is taken off'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
> 0) AND Process_active
expression: Process_maintenance_capacity <= Process_p_nom_max * Process_maintenance
Process_maintcap_lower_nommax:
description: '`Process-maintcap_lower_nommax` — in maintenance, the whole chosen build is taken off'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
> 0) AND Process_active
expression: Process_maintenance_capacity >= Process_p_nom_ext - Process_p_nom_max * (1 - Process_maintenance)
Process_maintcap_lower_nommin:
description: '`Process-maintcap_lower_nommin` — in maintenance, at least the floor of the build is
taken off'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_p_nom_extendable AND NOT (Process_committable AND Process_p_nom_mod
> 0) AND Process_active AND Process_p_nom_min > 0
expression: Process_maintenance_capacity >= Process_p_nom_min * Process_maintenance
Process_maint_status_le_status:
description: '`Process-maint-status-le-status` — the status in maintenance is at most the status'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_committable AND NOT Process_p_nom_extendable AND Process_active
expression: Process_maintenance_status <= Process_status
Process_maint_status_le_maint:
description: '`Process-maint-status-le-maint` — out of maintenance, the status in maintenance is zero'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_committable AND NOT Process_p_nom_extendable AND Process_active
expression: Process_maintenance_status <= Process_maintenance
Process_maint_status_lb:
description: '`Process-maint-status-lb` — on and in maintenance, the status in maintenance is one'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_committable AND NOT Process_p_nom_extendable AND Process_active
expression: Process_maintenance_status >= Process_status + Process_maintenance - 1
Process_maint_modstatus_le_status:
description: '`Process-maint-modstatus-le-status` — the modules on in maintenance are at most the
modules on'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_committable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_maintenance_status <= Process_status
Process_maint_modstatus_le_maint:
description: '`Process-maint-modstatus-le-maint` — out of maintenance, no module is on in maintenance;
in it, at most the modules the build cap holds'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_committable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_maintenance_status <= Process_p_nom_max / Process_p_nom_mod * Process_maintenance
Process_maint_modstatus_lb:
description: '`Process-maint-modstatus-lb` — in maintenance, every module on is on in maintenance'
dims: [scenario, snapshot, process]
where: Process_maintainable AND Process_committable AND Process_p_nom_mod > 0 AND Process_active
expression: Process_maintenance_status >= Process_status - Process_p_nom_max / Process_p_nom_mod *
(1 - Process_maintenance)
Bus_nodal_balance:
description: '`Bus-nodal_balance` — what is generated at a bus, storage dispatch and stores included,
less what the links take away, plus what arrives over them after losses and any delay at every port
they deliver to, each process port drawing or delivering at its own rate and each passive branch
carrying its flow, meets the load there, less half of every incident line''s and transformer''s
loss — PyPSA dissipates a branch''s loss half at either end. Each generator, storage unit, store
and load term enters with its component''s `sign` (`constraints.py:1428-1429`, `:1538`), and an
inactive load not at all. A bus nothing is attached to has no row; PyPSA refuses one that carries
load, and this file does not yet.'
dims: [scenario, snapshot, bus]
expression: Bus_injection == 0
expressions:
Generator_previous_status:
description: the commitment state a generator carries into a snapshot — the state it brought into
the horizon at the first, the previous snapshot's after that
dims: [scenario, snapshot, generator]
cases:
opening: {when: position(snapshot) == 0, expression: Generator_status_initial}
otherwise: shift(Generator_status, along=snapshot, offset=1)
Link_previous_status:
description: the commitment state a link carries into a snapshot — the state it brought into the horizon
at the first, the previous snapshot's after that
dims: [scenario, snapshot, link]
cases:
opening: {when: position(snapshot) == 0, expression: Link_status_initial}
otherwise: shift(Link_status, along=snapshot, offset=1)
Process_previous_status:
description: the commitment state a process carries into a snapshot — the state it brought into the
horizon at the first, the previous snapshot's after that
dims: [scenario, snapshot, process]
cases:
opening: {when: position(snapshot) == 0, expression: Process_status_initial}
otherwise: shift(Process_status, along=snapshot, offset=1)
total_cost:
dims: []
expression: ((Generator_capex + Link_capex) + Process_capex) + risk_weighted_opex
description: what the system costs — capacity once per active period at its expected cost over the
scenarios, operation in expectation over the scenarios, and a share of it at the tail
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
Generator_capex: {expression: sum(scenario_weight * Generator_p_nom_ext * Generator_capital_cost * Generator_capital_weight)}
Link_capex: {expression: sum(scenario_weight * Link_p_nom_ext * Link_capital_cost * Link_capital_weight)}
Process_capex: {expression: sum(scenario_weight * Process_p_nom_ext * Process_capital_cost * Process_capital_weight)}
risk_weighted_opex: {expression: '(1 - CVaR_omega) * sum(scenario_weight * scenario_opex, over=scenario)
+ CVaR_omega * CVaR'}
Generator_injection: {expression: 'sum(Generator_sign * Generator_p, by=Generator_bus, over=generator,
into=bus)'}
Link_injection: {expression: '-sum(Link_p, by=Link_bus0, over=link, into=bus) + sum(Link_output_arrival,
by=Link_output_bus, over=link_output, into=bus)'}
Load_injection: {expression: 'sum(Load_demand, by=Load_bus, over=load, into=bus)'}
Process_injection: {expression: 'sum(Process_output_arrival, by=Process_output_bus, over=process_output,
into=bus)'}
Link_output_arrival:
description: what a link delivers to an output port at a snapshot — its flow delayed by the port's
`delay` within its investment period, times the port's efficiency at the snapshot the flow arrives;
where the port is `cyclic_delay` the delayed flow wraps from the period's end, and where it is not
the flow still in transit at the period's first snapshots is lost. A port that does not delay (`delay`
zero) delivers its flow unshifted, cyclic or not
dims: [scenario, snapshot, link_output]
cases:
wrapping: {when: Link_output_cyclic_delay, expression: 'shift(at(Link_p, by=Link_output_link, over=link,
into=link_output), along=snapshot, offset=Link_output_delay, edge=''wrap'', by=snapshot_period,
within=period) * Link_efficiency'}
otherwise: shift(at(Link_p, by=Link_output_link, over=link, into=link_output), along=snapshot, offset=Link_output_delay,
edge=0, by=snapshot_period, within=period) * Link_efficiency
Process_output_arrival:
description: what a process transfers at a port at a snapshot — its internal power delayed by the
port's `delay` within its investment period, times the port's rate at the snapshot the transfer
arrives; where the port is `cyclic_delay` the delayed transfer wraps from the period's end, and
where it is not the energy still in transit at the period's first snapshots is lost. A port that
does not delay (`delay` zero) transfers at once, cyclic or not
dims: [scenario, snapshot, process_output]
cases:
wrapping: {when: Process_output_cyclic_delay, expression: 'shift(at(Process_p, by=Process_output_process,
over=process, into=process_output), along=snapshot, offset=Process_output_delay, edge=''wrap'',
by=snapshot_period, within=period) * Process_rate'}
otherwise: shift(at(Process_p, by=Process_output_process, over=process, into=process_output), along=snapshot,
offset=Process_output_delay, edge=0, by=snapshot_period, within=period) * Process_rate
scenario_opex:
dims: [scenario]
expression: ((((Generator_opex + Generator_commitment_opex) + Link_opex) + Link_commitment_opex) +
Process_opex) + Process_commitment_opex
description: what a future costs to run — every operating term, weighted by the snapshot's hours and
its period, before the scenario's own weight; a start and a stop cost what they cost, unweighted,
as PyPSA adds them (`optimize.py:414-429`)
Load_demand:
description: what a load draws from its bus's balance — its demand times its sign where it is active,
nothing where it is not, since PyPSA drops an inactive load from the balance (`constraints.py:1537-1538`)
dims: [scenario, snapshot, load]
cases:
active: {when: Load_active, expression: Load_sign * Load_p_set}
otherwise: 0
Generator_opex: {expression: 'sum(sum(((Generator_p * Generator_marginal_cost) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
over=snapshot) + sum(sum((((Generator_p * Generator_p) * Generator_marginal_cost_quadratic) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
over=snapshot)'}
Generator_commitment_opex: {expression: 'sum(sum(((Generator_status * Generator_stand_by_cost) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=generator),
over=snapshot) + sum(sum(Generator_start_up * Generator_start_up_cost, over=generator), over=snapshot)
+ sum(sum(Generator_shut_down * Generator_shut_down_cost, over=generator), over=snapshot)'}
Link_opex: {expression: 'sum(sum(((Link_p * Link_marginal_cost) * snapshot_weightings_objective) * at(period_weight_objective,
by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot) + sum(sum((((Link_p
* Link_p) * Link_marginal_cost_quadratic) * snapshot_weightings_objective) * at(period_weight_objective,
by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot)'}
Link_commitment_opex: {expression: 'sum(sum(((Link_status * Link_stand_by_cost) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=link), over=snapshot)
+ sum(sum(Link_start_up * Link_start_up_cost, over=link), over=snapshot) + sum(sum(Link_shut_down
* Link_shut_down_cost, over=link), over=snapshot)'}
Process_opex: {expression: 'sum(sum(((Process_p * Process_marginal_cost) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=process), over=snapshot)
+ sum(sum((((Process_p * Process_p) * Process_marginal_cost_quadratic) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), over=process), over=snapshot)'}
Process_commitment_opex: {expression: 'sum(sum(((Process_status * Process_stand_by_cost) * snapshot_weightings_objective)
* at(period_weight_objective, by=snapshot_period, over=period, into=snapshot), 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)'}
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),
**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_34_committable_maintenance.yaml', sources) as solution:
solution.objective # 6420.048611
The network, rung_34_committable_maintenance.py in the corpus — the spine plus what this rung adds:
# SPDX-FileCopyrightText: mathspec Contributors
#
# SPDX-License-Identifier: MIT
"""Rung 34: maintenance of committable units — a fixed, an extendable and a modular committable generator, link and process, each taken off for one event."""
from __future__ import annotations
import spine
def build():
"""The spine plus an east bus and nine maintainable committable components, with a dear peaker to cover them."""
n = spine.build()
n.add('Bus', 'east')
committable = {'committable': True, 'maintainable': True}
n.add(
'Generator',
'unit',
bus='north',
p_nom=60,
p_min_pu=0.3,
marginal_cost=5,
start_up_cost=10,
maintenance_duration=2,
**committable,
)
n.add(
'Generator',
'unit_ext',
bus='south',
p_nom_extendable=True,
p_nom_min=5,
p_nom_max=50,
capital_cost=10,
p_min_pu=0.2,
marginal_cost=4,
maintenance_duration=3,
maintenance_pu=0.5,
**committable,
)
n.add(
'Generator',
'unit_mod',
bus='south',
p_nom_extendable=True,
p_nom_mod=10,
p_nom_max=30,
capital_cost=8,
p_min_pu=0.5,
marginal_cost=3,
maintenance_duration=1,
**committable,
)
for component, ports in (('Link', {}), ('Process', {'rate0': -1.25})):
n.add(
component,
f'{component.lower()}_unit',
bus0='north',
bus1='east',
p_nom=40,
p_min_pu=0.2,
marginal_cost=1,
maintenance_duration=2,
**ports,
**committable,
)
n.add(
component,
f'{component.lower()}_ext',
bus0='south',
bus1='east',
p_nom_extendable=True,
p_nom_min=5,
p_nom_max=30,
capital_cost=5,
p_min_pu=0.2,
maintenance_duration=3,
maintenance_pu=0.5,
**ports,
**committable,
)
n.add(
component,
f'{component.lower()}_mod',
bus0='north',
bus1='east',
p_nom_extendable=True,
p_nom_mod=10,
p_nom_max=20,
capital_cost=3,
p_min_pu=0.5,
maintenance_duration=1,
**ports,
**committable,
)
n.add('Generator', 'east_peak', bus='east', p_nom=100, marginal_cost=60)
n.add('Load', 'east_load', bus='east', p_set=[50, 60, 40, 55])
return n
The data¶
Every table this spec declares was first declared by a lower rung; its values here are in the prep above.