Loads#

This file states PyPSA's Load. It is one of the 24 fragments that merge back into examples/pypsa.yaml. It adds a term to the sum Bus_injection.

given:
  expressions:
    Bus_injection: { dims: [bus, scenario, snapshot] }

dimensions:
  scenario:
    description: the futures dispatch is chosen in, each with a weight
  snapshot:
    description: dispatch periods
    dtype: datetime
    ordered: true
  bus:
    description: network nodes
  load:
    description: demands, each on one bus

relations:
  Load_bus:
    description: the bus a load sits on
    key: load
    values: bus

parameters:
  Load_p_set:
    description: demand
    dims: [scenario, snapshot, load]
  Load_sign:
    description: >-
      the sign a load's demand enters its bus's balance with — PyPSA's
      `sign`, `-1` unless given, `1` for a load that feeds its bus. PyPSA
      refuses one that differs by scenario (`constants.py:43`)
    dims: [load]
  Load_active:
    description: >-
      whether a load stands in the model — PyPSA's `active`. A load has no
      build year and no lifetime, so the flag holds in every snapshot. PyPSA
      refuses one that differs by scenario (`constants.py:51`)
    dims: [load]
    dtype: bool

expressions:
  Load_demand:
    description: >-
      what a load draws from its bus's balance — its demand times its sign
      where it is active, nothing where it is not, since PyPSA drops an
      inactive load from the balance (`constraints.py:1513-1514`)
    dims: [scenario, snapshot, load]
    cases:
      active: { when: Load_active, expression: Load_sign * Load_p_set }
    otherwise: 0
  Load_injection:
    expression: sum(Load_demand, over=load, by=Load_bus[bus])
    adds_to: Bus_injection

Given#

Symbol	Meaning
\(\mathit{Bus\_injection}\)	`Bus_injection` over \(\mathcal{N} \times \Xi \times \mathcal{T}\), an expression this file adds `Load_injection` to

Sets#

Symbol	Meaning
\(\mathcal{N}\)	index \(n\) — `bus` with \(\mathrm{Load\_bus}: \mathcal{D} \to \mathcal{N}\) — network nodes
\(\mathcal{D}\)	index \(d\) — `load` with \(\mathrm{Load\_bus}: \mathcal{D} \to \mathcal{N}\) — demands, each on one bus
\(\Xi\)	index \(\xi\) — `scenario` — the futures dispatch is chosen in, each with a weight
\(\mathcal{T}\)	index \(t\) — `snapshot` — dispatch periods

Parameters#

Symbol	Meaning
\(\mathrm{on}^{\mathrm{load}}\)	`Load_active` over \(\mathcal{D}\) — whether a load stands in the model — PyPSA's `active`. A load has no build year and no lifetime, so the flag holds in every snapshot. PyPSA refuses one that differs by scenario (`constants.py:51`)
\(\mathrm{load}\)	`Load_p_set` over \(\mathcal{D} \times \Xi \times \mathcal{T}\) — demand
\(\mathrm{sgn}^{\mathrm{load}}\)	`Load_sign` over \(\mathcal{D}\) — the sign a load's demand enters its bus's balance with — PyPSA's `sign`, `-1` unless given, `1` for a load that feeds its bus. PyPSA refuses one that differs by scenario (`constants.py:43`)

Definitions#

Symbol	Meaning
\(\check{\mathrm{load}}\)	`Load_demand` over \(\mathcal{D} \times \Xi \times \mathcal{T}\) — what a load draws from its bus's balance — its demand times its sign where it is active, nothing where it is not, since PyPSA drops an inactive load from the balance (`constraints.py:1513-1514`)
\(\mathrm{Load\_injection}\)	`Load_injection` over \(\mathcal{N} \times \Xi \times \mathcal{T}\)

Definitions#

Load_demand

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

Load_injection

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