A stochastic mixed-integer convex programming model for long-term distribution system expansion planning considering greenhouse gas emission mitigation

This paper proposes a multistage convex distribution system planning model to find the best reinforcement plan over a specified horizon. This strategy determines planning actions such as reinforcement of existing substations, conductor replacement of overloaded feeders, and siting and sizing of renewable and dispatchable distributed generation units. Besides, the proposed approach aims at mitigating the greenhouse gas emissions of electric power distribution systems via a monetary form. Inherently, this problem is a non-convex optimization model that can be an obstacle to finding the optimal global solution. To remedy this issue, convex envelopes are used to recast the original problem into a mixed integer conic programming (MICP) model. The MICP model guarantees convergence to optimal global solution by using existing commercial solvers. Moreover, to address the prediction errors in wind output power and electricity demands, a two-stage stochastic MICP model is developed. To validate the proposed model, detail analysis is carried out over various case studies of a 34-node distribution system under different conditions, while to show its potential and effectiveness a 135-node system with two substations is used. Numerical results confirm the effectiveness of the proposed planning scheme in obtaining an economic investment plan at the presence of several planning alternatives and to promote an environmentally committed electric power distribution network.