Title: Stochastic and Chance-Constrained Conic Distribution System Expansion Planning Using Bilinear Benders Decomposition,
Abstract: Second order conic programming (SOCP) has been used to model various
applications in power systems, such as operation and expansion planning. In
this paper, we present a two-stage stochastic mixed integer SOCP (MISOCP) model
for the distribution system expansion planning problem that considers
uncertainty and also captures the nonlinear AC power flow. To avoid costly
investment plans due to some extreme scenarios, we further present a
chance-constrained variant that could lead to cost-effective solutions. To
address the computational challenge, we extend the basic Benders decomposition
method and develop a bilinear variant to compute stochastic and
chance-constrained MISOCP formulations. A set of numerical experiments is
performed to illustrate the performance of our models and computational
methods. In particular, results show that our Benders decomposition algorithms
drastically outperform a professional MISOCP solver in handling stochastic
scenarios by orders of magnitude.