transport

A network: generators sit on buses, lines connect buses, and power balances at every bus.

The problem

\[\sum_{g \in \mathrm{bus}} p_{s,g} \;+\; \sum_{\ell \to b} f_{s,\ell} \;-\; \sum_{\ell \,\text{from}\, b} f_{s,\ell} \;=\; \ell_{s,b}\]

The model

dimensions:
  snapshot:
    dtype: int
  generator:
    dtype: str
    coords: [bus]           # every generator sits on a bus
  bus:
    dtype: str
  line:
    dtype: str
    coords: {from: bus, to: bus}   # both endpoints are buses

parameters:
  p_max:
    dims: [generator]
  cost:
    dims: [generator]
  cap:
    dims: [line]
  neg_cap:
    dims: [line]
  load:
    dims: [snapshot, bus]

variables:
  p:
    foreach: [snapshot, generator]
    bounds:
      lower: 0
      upper: p_max
  f:
    foreach: [snapshot, line]
    bounds:
      lower: neg_cap
      upper: cap

constraints:
  balance:
    foreach: [snapshot, bus]
    equations:
      - expression: group_sum(p, over=generator, by=bus) + group_sum(f, over=line, by=to) - group_sum(f, over=line, by=from) == load

objectives:
  total_cost:
    sense: minimize
    equations:
      - expression: p * cost

What it exercises

Three group_sum calls, and they are what a network is in this language. A dimension can carry coordinates — generator carries bus, line carries from and to — and group_sum(f, over=line, by=to) sums along a line's to coordinate, landing the result on bus. The same f is summed twice through two different coordinates, once as an inflow and once as an outflow.

No adjacency matrix, and no join written by the modeller: the topology is data on the dimension.

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examples/transport.yaml · back to all models