Benchmark Model

UnitCommitment.jl includes a reference Mixed-Integer Linear Programming (MILP), built with JuMP, which can either be used as-is to solve instances of the problem, or be extended to build more complex formulations.

Building and Solving the Model

Given an instance and a JuMP optimizer, the function build_model can be used to build the reference MILP model. For example:

using UnitCommitment, JuMP, Cbc
instance = UnitCommitment.load("ieee_rts/case118")
model = build_model(instance, with_optimizer(Cbc.Optimizer))

The model enforces all unit constraints described in Unit Commitment Instances, including ramping, minimum-up and minimum-down times. Some system-wide constraints, such as spinning reserves, are also enforced. The model, however, does not enforce transmission or N-1 security constraints, since these are typically generated on-the-fly.

A reference to the JuMP model is stored at model.mip. After constructed, the model can be optimized as follows:

optimize!(model.mip)

Decision Variables

References to all decision variables are stored at model.vars. A complete list of available decision variables is as follows:

Variable	Description
model.vars.production[gi,t]	Amount of power (in MW) produced by unit with index gi at time t.
model.vars.reserve[gi,t]	Amount of spinning reserves (in MW) provided by unit with index gi at time t.
model.vars.is_on[gi,t]	Binary variable indicating if unit with index gi is operational at time t.
model.vars.switch_on[gi,t]	Binary variable indicating if unit with index gi was switched on at time t. That is, the unit was not operational at time t-1, but it is operational at time t.
model.vars.switch_off[gi,t]	Binary variable indicating if unit with index gi was switched off at time t. That is, the unit was operational at time t-1, but it is no longer operational at time t.
model.vars.unit_cost[gi,t]	The total cost to operate unit with index gi at time t. Includes start-up costs, no-load costs and any other production costs.
model.vars.cost[t]	Total cost at time t.
model.vars.net_injection[bi,t]	Total net injection (in MW) at bus with index bi and time t. Net injection is defined as the total power being produced by units located at the bus minus the bus load.

Accessing the Solution

To access the value of a particular decision variable after the optimization is completed, the function JuMP.value(var) can be used. The following example prints the amount of power (in MW) produced by each unit at time 5:

for g in instance.units
    @show value(model.vars.production[g.index, 5])
end

Modifying the Model

Prior to being solved, the reference model can be modified by using the variable references above and conventional JuMP macros. For example, the following code can be used to ensure that at most 10 units are operational at time 4:

using UnitCommitment, JuMP, Cbc
instance = UnitCommitment.load("ieee_rts/case118")
model = build_model(instance, with_optimizer(Cbc.Optimizer))

@contraint(model.mip,
           sum(model.vars.is_on[g.index, 4]
               for g in instance.units) <= 10)

optimize!(model.mip)

It is not currently possible to modify the constraints included in the reference model.

Reference

@docs UnitCommitment.build_model