Sector

nimopt.models.sector has mixed density. The region-technology map is sparse: a technology exists in some regions and not in others. Every sited pair runs in every hour. The generation variable takes its members from a parameter over the sited pairs crossed with the whole horizon. It is therefore sparse in one axis and dense in the other.

minimize    Σ_{(r,k) sited, t} cost[r,k] · gen[r,k,t]
subject to  Σ_k gen[r,k,t] == demand[r,t]     for each region r and hour t
            0 ≤ gen[r,k,t] ≤ capacity[r,k]    for each sited (r,k) and hour t

from nimopt.models import sector

print(sector.definition().explain())

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Output

sector  min  not built
  sets        R · K · T
  parameters  sited (R,K,T) · capacity (R,K) · cost (R,K) · demand (R,T)
  variables   gen (R×K×T) over sited [0.0, capacity]
  constraint  balance (R,T)  Sum(K, gen[R, K, T]) == demand[R, T]
  objective   min  Sum(R, K, T, cost[R, K] * gen[R, K, T])

Each region meets its own demand from the technologies sited in it. The optimum is a merit order per region and hour.

from nimopt.models import sector

inputs = sector.data()
model = sector.definition().build(inputs)
solution = model.solve()
print(
    model.n_columns,
    "columns of a possible",
    len(inputs["R"]) * len(inputs["K"]) * len(inputs["T"]),
)
print(solution.objective, sector.reference(inputs))

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Output

16 columns of a possible 24
18350.0 18350.0

Every region-hour has a balance row. The capacity bound applies to the sited pairs alone, and no balance row is dropped.

from nimopt.models import sector

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

▶ Run this example

Output

balance  8 of 8 rows  stated by terms