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Loss tranches for a transmission line

Source: R/class-trade.R
lossTranches.Rd

Derive a piecewise-linear approximation of a line's quadratic losses, as a set of parallel capacity tranches with rising loss rates. [Experimental]

Usage

lossTranches(
  shares,
  loss = NULL,
  resistance = NULL,
  capacity = NULL,
  teff = 1,
  labels = NULL,
  fix = NULL,
  desc = NULL
)

Arguments

shares

numeric, the fraction of the line's capacity each tranche occupies. Must be positive and sum to 1. A single share reproduces the ordinary flat-teff line exactly.

loss

numeric, the loss fraction at rated load (dimensionless).

resistance, capacity

numeric, an alternative to loss: their product is the loss fraction at rated load. Both or neither.

teff

numeric, a base efficiency multiplied through every tranche, for losses that are not resistive (default 1).

labels

character, tranche names. Default T1, T2, ...

fix

numeric, a fixed line rating. When given, the result carries a capacity frame with cap.fx = shares * fix.

desc

character, per-tranche descriptions.

Value

An object of class loss_tranches: a list with cluster, trade and (optionally) capacity data frames, ready to pass to newACLine(), newDCLink() or newTrade().

Details

Returns the two (or three) data frames a trade object needs to describe the tranches: a cluster declaration carrying the shares, a trade frame carrying each tranche's teff, and – when fix is given – a capacity frame splitting a fixed rating between them.

The tranches are declared as fractions of the line's capacity rather than absolute quantities. That is what makes them invariant under parallel-circuit expansion, so they need no recomputation when capacity is optimised; see the loss-tranche note at the top of this file.

loss is the documented input: the dimensionless fraction of the sent flow lost when the line runs at its rating. It is the quantity the arithmetic actually needs, and the one that stays put under expansion. A resistance may be given instead, but only together with the capacity it was measured against, because loss = resistance * capacity – a resistance alone does not determine a loss fraction. The two must be in units whose product is dimensionless; for a per-unit resistance on base S_base, pass capacity = F / S_base.

See also

newACLine(), newDCLink(), newTrade()

Other class trade: newACLine(), newDCLink()

Examples

# A line losing 3% at full load, in three tranches
lossTranches(shares = c(0.4, 0.35, 0.25), loss = 0.03)
#> Loss tranches: 3 segment(s), 3% lost at rated load
#>  cluster share from   to   loss   teff
#>       T1  0.40 0.00 0.40 0.0120 0.9880
#>       T2  0.35 0.40 0.75 0.0345 0.9655
#>       T3  0.25 0.75 1.00 0.0525 0.9475
#> check: sum(share x loss) = 0.03  (= loss at rated load, 0.03)