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Description
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.
This example illustrates the AIMMS support for handling uncertainty in input data using Robust Optimization techniques, as discussed in the AIMMS Language Reference.
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:
i) the (smallest) box (2-dimensional interval) that contains all the initial scenario values
ii) the (largest) ellipsoid contained in the box from case i)
iii) 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.
Keywords
Uncertainty, Non-adjustable and Adjustable Decisions, Linear Decision Rules
Industries
Model Types
Linear Programming, Robust Optimization, Advanced Algorithms
References
Chapter 16 - A Power System Expansion Problem in the Optimization Modeling Guide
Download AIMMS Example
You can download an AIMMS example dealing with this problem via the link below, and run it after installing the AIMMS software. If you don't have an AIMMS license yet, you can download a free license of AIMMS.
ftp://ftp.aimms.com/pub/Download/Examples/Power System Expansion RO.aimmspack
Please make sure to save this file including the .aimmspack extension so that it can be opened by AIMMS.
This example application is a simplification of reality. Please do not hesitate to contact us to discuss how AIMMS enables you to build a complete optimization application that captures the full complexity of your problem.
Screenshot AIMMS Example
