Bayesian Framework for Multi-Stage Transmission Expansion Planning Under Uncertainty via Emulation

Effective transmission expansion planning is necessary to ensure a power system can satisfy all demand both reliably and economically. However, at the time reinforcement decisions are made many elements of the future power system background are uncertain, such as demand level, type and location of installed generators, and plant availability statistics. In the current power system planning literature, making decisions which account for such uncertainties is usually done by considering a small set of plausible scenarios, and the resulting limited coverage of parameter space limits confidence that the resulting decision will be a good one with respect to the real world. This thesis will consider a Bayesian approach to transmission expansion planning under uncertainty, which uses statistical emulators to approximate how input affects output of expensive simulators using a small number of training runs (evaluations from the simulator), as well as quantifying uncertainty in the simulator output for all points at which it has not been evaluated. In addition, expert judgement is used to formulate probability density functions to describe the uncertainties which exist in the power system, which can then be used alongside the emulator to estimate expected costs under uncertainty whilst also giving credible intervals for the resulting estimate. Further, the methodology will be expanded to consider multi-stage transmission expansion problems under uncertainty, where uncertainty can be reduced in various aspects of the power system between decisions. In the existing power system planning literature, multi-stage decisions under uncertainty are handled by considering a small number of possible projections of the future power system, which gives a very limited coverage of the space of all possible projections of the future power system. This thesis will consider how emulation can be used alongside backwards induction to calculate costs across all stages as a function of the first stage decision only, whilst also accounting for the uncertainties which exists in the future power system. As part of this, the future state of the power system is modelled using continuous variables which effectively allows for an infinite number of possible projections to be considered. Throughout this thesis, the methodology used is detailed in quite general terms, which should allow for the methodology to be applied to problems of interest other than the transmission expansion planning problem considered in this thesis with relative ease