Power System Expansion (with Robust Optimization)
This example implements a power system expansion model with uncertain electricity demand, covering a single time period. The problem is to determine new power plant design capacities in order to meet an increase in electricity demand. Yet, the future demand is uncertain. Initially, the uncertainty in the instantaneous demand is modeled by means of several demand scenarios.
In a Robust Optimization approach certain constraints are required to hold for every realization of the data within a given uncertainty set. In this example three choices for the uncertainty set corresponding to the instantaneous power demand are illustrated:
- the (smallest) box (2-dimensional interval) that contains all the initial scenario values;
- the (largest) ellipsoid contained in the box from case 1;
- the convex hull of the scenario values (that is, the smallest polyhedron containing all scenarios).
These sets are modeled by means of the Region (and Dependency) attribute of the corresponding uncertain parameters.
The same effect can be obtained by declaring explicit uncertainty constraints as those provided in the "Auxiliary Uncertainty" declaration section, for illustration, and including the necessary uncertainty constraints in the set of uncertainty constraints to be considered for the generation of the robust model.
There is a distinction made between non-adjustable decisions (that is, the design of new capacity) and the adjustable decisions (that is, the capacity allocation and the electricity import decisions). The adjustable decisions are assumed to follow linear decision rules depending on the values of the required electricity parameter.
The approach illustrated here is based on the special Robust Optimization features offered by AIMMS through the GMP library.
Linear Program, Uncertainty, Robust Optimization, Non-adjustable and Adjustable Decisions, Linear Decision Rules.
A zip file with this example can be downloaded here.