# Stochastic and Chance-Constrained Conic Distribution System Expansion Planning Using Bilinear Benders Decomposition

## TL;DR

This paper introduces a stochastic mixed-integer second order conic programming model for distribution system expansion planning that incorporates uncertainty, nonlinear power flow, and chance constraints, solved efficiently with a novel bilinear Benders decomposition.

## Contribution

It develops a bilinear Benders decomposition method for stochastic and chance-constrained MISOCP models in power system planning, improving computational efficiency.

## Key findings

- Benders decomposition outperforms standard solvers by orders of magnitude.
- Chance-constrained approach reduces costly extreme scenario investments.
- Model effectively captures nonlinear AC power flow under uncertainty.

## 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.