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Nodal

nimopt.models.nodal groups generators into buses through a lookup parameter. at[G, B] has an entry where generator g is located at bus b. Multiplying the generation by it maps a row over generators to a row over buses. The coefficient introduces B, a dimension no variable has, and the balance is indexed over the dimensions the lookup defines.

minimize    Σ_{t,g} cost[g] · gen[t,g]
subject to  Σ_g at[g,b] · gen[t,g] == demand[b,t]    for each bus b and hour t
            0 ≤ gen[t,g] ≤ p_max[g]
from nimopt.models import nodal

print(nodal.definition().explain())
Run this example
Output
nodal  min  not built
  sets        T · G · B
  parameters  at (G,B) · p_max (G) · cost (G) · demand (B,T)
  variables   gen (T×G) [0.0, p_max]
  constraint  balance (B,T)  Sum(G, at[G, B] * gen[T, G]) == demand[B, T]
  objective   min  Sum(T, G, cost[G] * gen[T, G])

Each bus meets its own demand from the generators sited at it. The optimum is a merit order per bus and hour.

from nimopt.models import nodal

inputs = nodal.data()
solution = nodal.definition().build(inputs).solve()
print(solution.objective, nodal.reference(inputs))
Run this example
Output
11850.0 11850.0

Every bus-hour has a row. A generator sited elsewhere is a term the lookup removes from that row, not a row that is dropped.

from nimopt.models import nodal

model = nodal.definition().build(nodal.data())
print(model.absent("balance"))
Run this example
Output
balance  6 of 6 rows  stated by terms
  term absent G='g0_0', B='b1_0', T=0  gen  absent-coefficient (at)
  term absent G='g0_0', B='b1_0', T=1  gen  absent-coefficient (at)
  term absent G='g0_0', B='b1_0', T=2  gen  absent-coefficient (at)
  term absent G='g1_0', B='b1_0', T=0  gen  absent-coefficient (at)
  term absent G='g1_0', B='b1_0', T=1  gen  absent-coefficient (at)
  term absent G='g1_0', B='b1_0', T=2  gen  absent-coefficient (at)
  term absent G='g2_0', B='b0_0', T=0  gen  absent-coefficient (at)
  term absent G='g2_0', B='b0_0', T=1  gen  absent-coefficient (at)
  term absent G='g2_0', B='b0_0', T=2  gen  absent-coefficient (at)
  term absent G='g3_0', B='b0_0', T=0  gen  absent-coefficient (at)
  term absent G='g3_0', B='b0_0', T=1  gen  absent-coefficient (at)
  term absent G='g3_0', B='b0_0', T=2  gen  absent-coefficient (at)