Multistage stochastic capacity planning of survivable electricity distribution networks

Abstract

An electricity distribution network transports electrical power from the drop-off points of the national transmission network to local customers. The capacity of the distribution network must be expanded to cope with uncertain future outcomes, such as increasing demand, and to ensure the network has adequate reserve capacity to enable restoration of power to consumers (by switching in reserve lines) if some single line fails. This thesis develops a formulation and a solution procedure, constituting a solution approach, for solving instances of a capacity-planning model for an electricity distribution network that considers uncertainty in future outcomes and reserve capacity (survivability) requirements over a multistage planning horizon. We refer to the model as the multistage stochastic capacity-planning and survivable network design model, CP-SND. This model has, as a special case, a set of other capacity-planning models, namely, a restoration model, a two-stage survivable network design model (SND), and a multistage stochastic capacity-planning model (OP). The thesis develops formulations and solution procedures for these models and uses them as building blocks to devise those for the CP-SND model. All models minimize the total capacityexpansion and operational cost, and the stochastic models use scenario representation of uncertainty. Modular capacity expansions and the discrete operational requirements in these models give rise to difficult mixed-integer programs (MIPs). Hence, much of the literature either focuses on heuristic solution approaches, which cannot guarantee the quality of a solution, or proposes mathematical formulations that are tractable only for small instances. All problem instances that we use for computational testing of the solution approaches in this thesis are based on a real network that is part of the local distribution network in Auckland, New Zealand. We develop mathematicalprogramming solution approaches that can solve realistic instances and guarantee the quality of a solution. Capacity expansions require capital investments typically in the order of millions, thus savings from optimizing plans can be significant.