Loads#

One of the 24 fragments of examples/pypsa.yaml: PyPSA's Load. It adds a term to Bus_injection.

dimensions:
  scenario:
    description: the futures dispatch is chosen in, each with a weight
  snapshot:
    description: dispatch periods
    dtype: datetime
  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 (`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

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

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:1537-1538`)
    dims: [scenario, snapshot, load]
    cases:
      active: { when: Load_active, expression: Load_sign * Load_p_set }
    otherwise: 0
  Load_injection: sum(Load_demand, by=Load_bus, over=load, into=bus)

Sets#

Symbol	Meaning
\(\Xi\)	index \(\xi\) — `scenario` — the futures dispatch is chosen in, each with a weight
\(\mathcal{T}\)	index \(t\) — `snapshot` — dispatch periods
\(\mathcal{N}\)	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

Parameters#

Symbol	Meaning
\(\mathrm{load}\)	`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`)

Given#

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

Definitions#

Symbol	Meaning
\(\check{\mathrm{load}}\)	`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`)
\(\mathrm{Load\_injection}\)	`Load_injection` over \(\Xi \times \mathcal{T} \times \mathcal{N}\)

Definitions#

Load_demand

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

Load_injection

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