Joint Chance Constraints achieve a good trade-off between cost and robustness for optimization under uncertainty. This talk proposes a Julia implementation of Joint Chance Constraints and algorithms to solve the programming problems for different types of multivariate probabilities. The library focuses on unit commitment problems for decentralized, renewable-powered microgrids, connected to an unreliable higher-level, grid-balancing unit, but can be applied to similarly-structured problems.
Ensuring a certain level of reliability becomes challenging with renewable-powered and decentralized energy systems. The problem is increasingly relevant for energy system dispatch planning, both in cases of advanced grid infrastructure or of severe resource-constraints. The capability of a local unit of balancing its supply and demand successfully becomes crucial, when the availability of a higher-level grid-balancing unit is unreliable.
In this talk, I explain how this unreliability can be considered using Joint Chance Constraints and will introduce how these are implemented in JuMP optimization models. By comparing these models to both deterministic and Individual Chance Constrained programming problems, I prove that Joint Chance Constraints help increase the reliability of the microgrids and their successful operation in the "islanded" mode.
The library was conceived for the application described above, but is written generically such that it can be applied for other similarly-structured problems.