Link¶

The Link components are used for controllable directed flows between two or more buses with arbitrary energy carriers (bus0, bus1, bus2, etc.). For instance, they can represent point-to-point HVDC links, unidirectional lossy HVDC links, converters between AC and DC, net transfer capacities (NTCs) of HVAC lines (neglecting Kirchhoff's voltage law), as well as any conversion between carriers (e.g. electricity to hydrogen in electrolysis, electricity to heat in heat pumps, or gas to electricity and heat in a combined heat and power (CHP) plant).

The Link component has one dispatch variable p0 associated with the input from bus0 (positive if withdrawing from bus0) and one or more outputs p1, p2, etc. associated with the output at bus1, bus2, etc. (negative if supplying to these buses). The outputs at bus1, bus2, etc. are proportional to the input at bus0 multiplied by the corresponding efficiency (e.g. efficiency, efficiency2, etc.). That means that the link can have multiple outputs in fixed ratio to the input.
The columns bus2, efficiency2, bus3, efficiency3, etc. in n.links are automatically added to the component attributes.
Any marginal_cost are related to the input p0 at bus0 (e.g. cost per unit of fuel consumed rather than cost per unit of electricity produced for a power plant).
For links with multiple inputs in fixed ratio to one of the inputs, you can define the other inputs as outputs with a negative efficiency so that they withdraw from the corresponding bus if there is a positive flow for p0.
For delayed energy transport, use the attribute delay, delay2, ... which postpones the output at bus1, bus2, ... in terms of elapsed time, taking snapshot weightings into account. See this example.

When to use Line instead?

Use the Line component type for power lines for which their power flow is determined passively through Kirchhoff's voltage law.

Link with bidirectional lossless flow

Because the Link component can have efficiency losses and marginal costs, the default settings allow only for flow in one direction (p_min_pu=0), from bus0 to bus1. To build a bidirectional lossless link, set efficiency = 1, marginal_cost = 0 and p_min_pu = -1.

n.add(
    "Link",
    "bidirectional-link",
    bus0="bus-A",
    bus1="bus-B",
    p_nom=1000,
    efficiency=1,
    marginal_cost=0,
    p_min_pu=-1,
)

Link with a single input and multiple outputs

Suppose a link representing a combined heat and power (CHP) plant takes as input 1 unit of fuel and gives as outputs 0.3 units of electricity and 0.7 units of heat. Then bus0 connects to the fuel, bus1 connects to electricity with efficiency=0.3 and bus2 connects to heat with efficiency2=0.7. This example illustrates a CHP with a fixed power-heat ratio using links.

n.add(
    "Link",
    "CHP",
    bus0="gas",
    bus1="electricity",
    bus2="heat",
    efficiency=0.3,    # 0.3 units of electricity per unit of gas
    efficiency2=0.7,   # 0.7 units of heat per unit of gas
    p_nom_extendable=True,
    capital_cost=50,   # cost per MW of gas input
)

Link with multiple inputs and a single output

Suppose a link representing a methanation process takes as inputs one unit of hydrogen and 0.5 units of carbon dioxide, and gives as outputs 0.8 units of methane and 0.2 units of heat. Then bus0 connects to hydrogen, bus1 connects to carbon dioxide with efficiency=-0.5 (since 0.5 units of carbon dioxide is taken for each unit of hydrogen), bus2 connects to methane with efficiency2=0.8 and bus3 to heat with efficiency3=0.2. This example illustrates many modelling processes with multiple inputs and outputs using links.

n.add(
    "Link",
    "methanation",
    bus0="hydrogen",
    bus1="CO2",
    bus2="methane",
    bus3="heat",
    efficiency=-0.5,   # consumes 0.5 units of CO2 per unit of hydrogen
    efficiency2=0.8,   # produces 0.8 units of methane
    efficiency3=0.2,   # produces 0.2 units of heat
    p_nom_extendable=True,
    capital_cost=100,  # cost per MW of hydrogen input
)

attribute	type	unit	default	description	status
name	string	nan	nan	Unique name	Input (required)
bus0	string	nan	nan	Name of origin bus to which link is attached.	Input (required)
bus1	string	nan	nan	Name of first destination bus to which link is attached. Further destination buses (`bus2`, `bus3`, etc.) are automatically expanded as needed.	Input (required)
type	string	nan	nan	Placeholder for link type. Not implemented.	Input (optional)
carrier	string	nan	nan	Carrier of the link describing its technology (e.g. gas boiler, electrolyser, HVDC link).	Input (optional)
efficiency	static or series	per unit	1	Efficiency of energy transfer from `bus0` to `bus1`. Can be time-dependent (e.g. to represent temperature-dependent heat pump COP). Further efficiency attributes for further buses (e.g. `bus2`, `bus3`, etc.) are automatically expanded as needed (e.g. `efficiency2`, `efficiency3`, etc.).	Input (optional)
active	boolean	nan	True	Whether to consider the component in basic functionality or not	Input (optional)
build_year	int	year	0	Build year	Input (optional)
lifetime	float	years	inf	Lifetime	Input (optional)
p_nom	float	MW	0	Limit of power which can pass through link (in units of `bus0`). Ignored if `p_nom_extendable=True`.	Input (optional)
p_nom_mod	float	MW	0	Unit size of link module (e.g. fixed blocks of 100 MW).	Input (optional)
p_nom_extendable	boolean	nan	False	Switch to allow capacity `p_nom` to be extended.	Input (optional)
p_nom_min	float	MW	0	If `p_nom_extendable=True`, set its minimum value.	Input (optional)
p_nom_max	float	MW	inf	If `p_nom_extendable=True`, set its maximum value.	Input (optional)
p_nom_set	float	MW	nan	If `p_nom` is extendable in optimization, set its value.	Input (optional)
p_set	static or series	MW	nan	The dispatch set point for `p0` of the link (for optimisation and power flow).	Input (optional)
p_init	static	MW	nan	Active power used as a starting point for limiting the ramp in the very first snapshot (for optimisation)	Input (optional)
p_min_pu	static or series	per unit of p_nom	0.	Minimal dispatch per unit of `p_nom` for the link. Can also be negative.	Input (optional)
p_max_pu	static or series	per unit of p_nom	1.	Maximal dispatch per unit of `p_nom` for the link. Can also be negative.	Input (optional)
capital_cost	float	currency/MW	0	Fixed period costs of extending `p_nom` by 1 MW (unit of `bus0`, e.g. annuitized investment costs). Used directly unless `overnight_cost` is specified. Any `length` factor must already be included.	Input (optional)
overnight_cost	float	currency/MW	nan	Overnight (upfront) investment cost per MW (unit of `bus0`). If specified, PyPSA calculates annuity using `discount_rate` and `lifetime`. Takes precedence over `capital_cost`.	Input (optional)
discount_rate	float	per unit	nan	Discount rate for annuity calculation when using `overnight_cost`. Supports 0% rate (simple depreciation).	Input (optional)
fom_cost	float	currency/MW	0	Fixed period operation and maintenance costs per MW (unit of `bus0`), added to annuitized investment cost.	Input (optional)
marginal_cost	static or series	currency/MWh	0.	Marginal cost of 1 MWh consumption from `bus0` (e.g. including variable operation and maintenance costs of an electrolyser but excluding electricity costs).	Input (optional)
marginal_cost_quadratic	static or series	currency/MWh	0.	Quadratic marginal cost for 1 MWh of consumption from `bus0`.	Input (optional)
stand_by_cost	static or series	currency/h	0.	Stand-by cost for operating the link. This cost is incurred whenever the status is 1 (including when dispatch decision is zero).	Input (optional)
length	float	km	0	Length of the link. Useful for calculating `capital_cost` for HVDC connections.	Input (optional)
terrain_factor	float	per unit	1	Terrain factor for increasing `capital_cost` calculated from `length`.	Input (optional)
committable	boolean	nan	False	Apply unit commitment constraints.	Input (optional)
start_up_cost	float	currency	0	Cost to start up the link. Only used if `committable=True`.	Input (optional)
shut_down_cost	float	currency	0	Cost to shut down the link. Only used if `committable=True`.	Input (optional)
min_up_time	int	snapshots	0	Minimum number of snapshots for status to be 1. Only used if `committable=True`. Does not consider snapshot weightings.	Input (optional)
min_down_time	int	snapshots	0	Minimum number of snapshots for status to be 0. Only used if `committable=True`. Does not consider snapshot weightings.	Input (optional)
up_time_before	int	snapshots	1	Number of snapshots that the link was online before network.snapshots start. Only read if `committable=True` and `min_up_time>0`. Does not consider snapshot weightings.	Input (optional)
down_time_before	int	snapshots	0	Number of snapshots that the link was offline before network.snapshots start. Only read if `committable=True` and `min_down_time>0`. Does not consider snapshot weightings.	Input (optional)
ramp_limit_up	static or series	per unit	nan	Maximum increase from one snapshot to the next, per unit of `p_nom`. Ignored if NaN. Does not consider snapshot weightings.	Input (optional)
ramp_limit_down	static or series	per unit	nan	Maximum decrease from one snapshot to the next, per unit of `p_nom`. Ignored if NaN. Does not consider snapshot weightings.	Input (optional)
ramp_limit_start_up	float	per unit	nan	Maximum increase at start up, per unit of `p_nom`. Only used if `committable=True`. Ignored if NaN.	Input (optional)
ramp_limit_shut_down	float	per unit	nan	Maximum decrease at shut down, per unit of `p_nom`. Only used if `committable=True`. Ignored if NaN.	Input (optional)
delay	int	snapshot weighting units	0	Delay of energy delivery to `bus1` in units of `n.snapshot_weightings.generators`. Energy withdrawn from `bus0` at snapshot `t` arrives at the first snapshot whose cumulative generator weighting start is at least `delay` units later. Auto-expanded as `delay2`, `delay3`, etc. for additional ports.	Input (optional)
cyclic_delay	boolean	nan	True	Whether delayed energy wraps cyclically from end to start of the optimization period. If False, energy is lost at the tail and first snapshots receive nothing from delayed links. Auto-expanded as `cyclic_delay2`, `cyclic_delay3`, etc. for additional ports.	Input (optional)
p	series	MW	0.	Internal power (positive if link is withdrawing from `bus0`).	Output
p0	series	MW	0.	Power at `bus0` (positive if link is withdrawing from `bus0`).	Output
p1	series	MW	0.	Power at `bus1` (positive if link is withdrawing from `bus1`).	Output
p_nom_opt	float	MW	0	Optimised nominal capacity.	Output
status	series	nan	1.	Status in the snapshot (1 is on, 0 is off). Only returned if `committable=True`.	Output
start_up	series	nan	1.	Whether the unit was started in the snapshot (1 is yes, 0 is no). Only returned if `committable=True`.	Output
shut_down	series	nan	1.	Whether the unit was shut down in the snapshot (1 is yes, 0 is no). Only returned if `committable=True`.	Output
mu_lower	series	currency/MW	nan	Shadow price of lower `p_nom` limit \(-F \leq f\). Always non-negative.	Output
mu_upper	series	currency/MW	nan	Shadow price of upper `p_nom` limit \(f \leq F\). Always non-negative.	Output
mu_p_set	series	currency/MWh	nan	Shadow price of fixed dispatch `p_set`	Output
mu_ramp_limit_up	series	currency/MWh	nan	Shadow price of upper ramp up limit	Output
mu_ramp_limit_down	series	currency/MWh	nan	Shadow price of lower ramp down limit	Output