Dispatch

nimopt.models.dispatch is least-cost dispatch of a generator fleet against a load. One variable p is indexed over snapshots and generators, there is one balance row per snapshot, and each generator has a cost. Every other model in the corpus adds one axis to this one.

minimize    Σ_{t,g} cost[g] · p[t,g]
subject to  Σ_g p[t,g] == load[t]        for each snapshot t
            0 ≤ p[t,g] ≤ p_max[g]

The balance row has no coefficient. A sum over a dimension requires none, and the corpus writes no coefficient a model does not require.

from nimopt.models import dispatch

print(dispatch.definition().explain())

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Output

dispatch  min  not built
  sets        snapshot · generator
  parameters  p_max (generator) · load (snapshot) · cost (generator)
  variables   p (snapshot×generator) [0.0, p_max]
  constraint  balance (snapshot)  Sum(generator, p[snapshot, generator]) == load[snapshot]
  objective   min  Sum(snapshot, generator, cost[generator] * p[snapshot, generator])

Snapshots are independent, and the optimum is the merit order per snapshot. reference computes it without a solver.

from nimopt.models import dispatch

inputs = dispatch.data()
solution = dispatch.definition().build(inputs).solve()
print(solution.status)
print(solution.objective, dispatch.reference(inputs))

▶ Run this example

Output

optimal
1920.0 1920.0

The balance row is produced for every snapshot in the load, and absent reports no dropped row.

from nimopt.models import dispatch

model = dispatch.definition().build(dispatch.data())
print(model.absent("balance"))

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Output

balance  6 of 6 rows  stated by terms