Write a piecewise curve out by hand

Tie a number of flows to one curve where that number is data: a boiler ties two flows and a CHP unit ties three, in one model. A piecewise: block lists its links in the file, so it cannot say this. The formulation written out can.

1. Declare the weights as a variable over the breakpoint dimension, masked to how far each curve runs:

variables:
  weight: # the convex combination, one per converter and period
    dims: [converter, time, bp]
    where: bp_present # how far each curve runs
    bounds: { lower: 0, upper: 1 }

2. Restrict the weights with an sos: block. type: 2 states the restriction that method: sos2 emits:

sos:
  on_one_segment: { variable: weight, over: bp, type: 2 }

3. Write the convexity row, and one row per flow. The row per flow is where the count goes, and a relation carries it:

constraints:
  one_operating_point:
    dims: [converter, time]
    expression: sum(weight, over=bp) == 1
  on_the_curve: # one row per flow
    dims: [flow, time]
    expression: rate == sum(at(weight, by=converter_of, over=converter, into=flow) * bp_rate, over=bp)

A converter with a fourth flow is then a row in a table.