Power flow#

given:
  expressions:
    Cycle_angle_sum:
      dims: [cycle, scenario, snapshot]
      description: >-
        the voltage angle differences around a cycle: every branch flow times
        its cycle weight, and every transformer phase shift

dimensions:
  scenario:
    description: the futures dispatch is chosen in, each with a weight
  snapshot:
    description: dispatch periods
    dtype: datetime
    ordered: true
  cycle:
    description: >-
      independent cycles of the passive network graph, the cycle basis, data
      prep. Each period has its own basis, of the branches that are active in it. A
      label is a position in that period's basis, so one label is a different
      cycle in another period
  period:
    description: investment periods. It is PyPSA's `investment_periods`
    dtype: int
    ordered: true

maps:
  snapshot:
    period:
      description: the investment period a snapshot falls in
      refers_to: period

parameters:
  Cycle_in_basis:
    description: >-
      whether a period's cycle basis reaches the cycle label, data prep. A
      label beyond the basis of the period has no Kirchhoff voltage law row
    dims: [period, cycle]
    dtype: bool

constraints:
  Kirchhoff_Voltage_Law:
    description: >-
      `Kirchhoff-Voltage-Law` — around every independent cycle the
      impedance-weighted flows sum to nothing. This makes the linear power
      flow physical rather than transport. A transformer's flow weighs its
      effective reactance, and its phase shift enters the cycle sum too. The
      shift is a constant where it is fixed. Where a phase-shifting
      transformer chooses its shift, it is the shift decision times its cycle
      weight. A snapshot uses the cycles of its own period, of the branches
      that are active in it (`constraints.py:1710-1729`). A cycle label that
      period's basis does not reach has no row
    dims: [scenario, snapshot, cycle]
    where: at(Cycle_in_basis, by=snapshot[period])
    expression: Cycle_angle_sum == 0