Models and applications of stochastic programming with decision-dependent uncertainty in power systems: A review

Stochastic programming is a competitive tool in power system uncertainty management. Traditionally, stochastic programming assumes uncertainties to be exogenous and independent of decisions. However, there are situations where statistical features of uncertain parameters are not constant but dependent on decisions, classifying such uncertainties as decision-dependent uncertainty (DDU). This is particularly the case with future power systems highly penetrated by multi-source uncertainties, where planning or operation decisions might exert unneglectable impacts on uncertainty features. This paper reviews the stochastic programming with DDU, especially those applied in the field of power systems. Mathematical properties of diversified types of DDU in stochastic programming are introduced, and a comprehensive review on sources and applications of DDU in power systems is presented. Then, focusing on a specific type of DDU, that is, decision-dependent probability distributions, a taxonomy of available modelling techniques and solution approaches for stochastic programming with this type of DDU and different structural features are presented and discussed. Eventually, the outlook of two-stage stochastic programming with DDU for future power system uncertainty management is explored, including both exploring the applications and developing efficient modelling and solution tools.