01 · Minimum-cost load curtailment

Scenario. A radial feeder connects a substation (Bus 0) to two loads via two line segments. Bus 1 serves a small factory (0.6 MW); Bus 2 serves a warehouse (0.4 MW). An upstream fault limits the substation connection to at most 0.6 MW — far less than the combined 1.0 MW demand. Some load must be shed.

Interrupting the factory costs 30 monetary units/MW (critical production process); interrupting the warehouse costs only 5 units/MW (deferrable refrigeration). The optimiser finds the cheapest curtailment plan.

Tip

For a ready-made one-call load-shedding interface see Load shedding. This tutorial builds the problem from scratch to show the full API.

Building the network

import monee.express as mx
import monee.model as mm
import monee.problem as mp
from monee import run_energy_flow_optimization

net = mx.create_multi_energy_network()

# Three buses on a radial feeder: substation → factory → warehouse
bus_sub = mx.create_bus(net)
bus_fac = mx.create_bus(net)
bus_wh  = mx.create_bus(net)

mx.create_line(net, bus_sub, bus_fac, 1000, r_ohm_per_m=7e-5, x_ohm_per_m=7e-5)
mx.create_line(net, bus_fac, bus_wh,  1000, r_ohm_per_m=7e-5, x_ohm_per_m=7e-5)

mx.create_ext_power_grid(net, bus_sub)

fac_id = mx.create_power_load(net, bus_fac, p_mw=0.6, q_mvar=0.0)
wh_id  = mx.create_power_load(net, bus_wh,  p_mw=0.4, q_mvar=0.0)

# Attach penalty and nominal demand as plain attributes on the model objects.
# These are read by the objective at solve time.
fac_model = net.child_by_id(fac_id).model
wh_model  = net.child_by_id(wh_id).model

fac_model._penalty   = 30   # high: critical process
fac_model._p_nominal = 0.6  # MW
wh_model._penalty    = 5    # low: deferrable
wh_model._p_nominal  = 0.4  # MW

Defining the optimisation problem

An OptimizationProblem has three building blocks:

  • Controllables — which attributes the solver may vary (here: the regulation fraction of each load).

  • Constraints — additional restrictions beyond the energy-flow equations (here: the 0.6 MW substation limit).

  • Objective — the scalar to minimise (here: total curtailment cost).

problem = mp.OptimizationProblem()

# ── Controllables ──────────────────────────────────────────────────────────
# regulation ∈ [0, 1]: fraction of each load that remains served.
# 1 = fully served, 0 = completely curtailed.
problem.controllable_demands([
    (
        "regulation",
        mp.AttributeParameter(
            min=lambda attr, val: 0,
            max=lambda attr, val: 1,
            val=lambda attr, val: 1,   # initialise at full service
        ),
    )
])

# ── Constraint ─────────────────────────────────────────────────────────────
# The substation can inject at most 0.6 MW (upstream fault limit).
constraints = mp.Constraints()
constraints.select_types(mm.ExtPowerGrid).equation(
    lambda model: model.p_mw <= 0.6
)
problem.constraints = constraints

# ── Objective ──────────────────────────────────────────────────────────────
# Minimise total curtailment cost:
#   cost = Σ (1 - regulation_i) × p_nominal_i × penalty_i
#
# The penalty attributes were stored on the model objects above.
# At solve time model.regulation is a solver variable; the expression
# (1 - model.regulation) is therefore part of the optimisation problem.
objectives = mp.Objectives()
objectives.select(
    lambda model: isinstance(model, mm.PowerLoad) and hasattr(model, "_penalty")
).data(
    lambda model: (1 - model.regulation) * model._p_nominal * model._penalty
).calculate(
    lambda model_to_data: sum(model_to_data.values())
)
problem.objectives = objectives

Running the optimisation

result = run_energy_flow_optimization(net, problem)
print(f"Objective (curtailment cost): {result.objective:.2f}")

 Objective (curtailment cost): 2.00

The objective value of 2.00 matches the expected optimum: curtail the entire warehouse (0.4 MW × penalty 5 = 2.0 units), which is far cheaper than reducing the factory.

Inspecting results

get() returns the result DataFrame for a given model type:

load_df = result.get(mm.PowerLoad)
print(load_df[["p_mw", "regulation"]].round(3))

    p_mw  regulation
 0   0.6       1.000
 1   0.0       0.000

The factory (row 0) keeps its full 0.6 MW at regulation = 1.0. The warehouse (row 1) is completely curtailed to regulation = 0.0. The substation import equals exactly the 0.6 MW limit:

ext_df = result.get(mm.ExtPowerGrid)
print(f"Substation import: {ext_df['p_mw'].sum():.2f} MW")

 Substation import: 0.60 MW

Note

Removing debug=False (the default) from OptimizationProblem keeps the solver output quiet. Pass debug=True while developing to see which attributes were made controllable.

Next steps