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JuMP Model

In this page, we describe the JuMP optimization model produced by the function UnitCommitment.build_model. A detailed understanding of this model is not necessary if you are just interested in using the package to solve some standard unit commitment cases, but it may be useful, for example, if you need to solve a slightly different problem, with additional variables and constraints.

The notation in this page generally follows [KnOsWa20].

Decision variables

Generators

Name	Symbol	Description	Unit
`is_on[g,t]`	`u_{g}(t)`	True if generator `g` is on at time `t`.	Binary
`switch_on[g,t]`	`v_{g}(t)`	True is generator `g` switches on at time `t`.	Binary
`switch_off[g,t]`	`w_{g}(t)`	True if generator `g` switches off at time `t`.	Binary
`prod_above[g,t]`	`p'_{g}(t)`	Amount of power produced by generator `g` above its minimum power output at time `t`. For example, if the minimum power of generator `g` is 100 MW and `g` is producing 115 MW of power at time `t`, then `prod_above[g,t]` equals `15.0`.	MW
`segprod[g,t,l]`	`p^l_g(t)`	Amount of power from piecewise linear segment `l` produced by generator `g` at time `t`. For example, if cost curve for generator `g` is defined by the points `(100, 1400)`, `(110, 1600)`, `(130, 2200)` and `(135, 2400)`, and if the generator is producing 115 MW of power at time `t`, then `segprod[g,t,:]` equals `[10.0, 5.0, 0.0]`.	MW
`reserve[g,t]`	`r_g(t)`	Amount of reserves provided by generator `g` at time `t`.	MW
`startup[g,t,s]`	`\delta^s_g(t)`	True if generator `g` switches on at time `t` incurring start-up costs from start-up type `s`.	Binary

Buses

Name	Symbol	Description	Unit
`net_injection[b,t]`	`n_b(t)`	Net injection at bus `b` at time `t`.	MW
`curtail[b,t]`	`s^+_b(t)`	Amount of load curtailed at bus `b` at time `t`	MW

Price-sensitive loads

Name	Symbol	Description	Unit
`loads[ps,t]`	`d_{ps}(t)`	Amount of power served to price-sensitive load `ps` at time `t`.	MW

Transmission lines

Name	Symbol	Description	Unit
`flow[l,t]`	`f_l(t)`	Power flow on line `l` at time `t`.	MW
`overflow[l,t]`	`f^+_l(t)`	Amount of flow above the limit for line `l` at time `t`.	MW


Since transmission and N-1 security constraints are enforced in a lazy way, most of the variables `flow[l,t]` and `overflow[l,t]` are never added to the model. Accessing `model[:flow][l,t]`, for example, without first checking that the variable exists will generate an error.

Objective function


\begin{align*}
    \text{minimize} \;\; &
        \sum_{s \in PS} x
\end{align*}

Constraints

Querying the model

Modifying the model

Adding new constraints

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Removing existing constraints

References

[KnOsWa20] Bernard Knueven, James Ostrowski and Jean-Paul Watson. "On Mixed-Integer Programming Formulations for the Unit Commitment Problem". INFORMS Journal on Computing (2020). DOI: 10.1287/ijoc.2019.0944

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