Second-Order Cone Programming for Linepack in Multistage Stochastic Co-Expansion Planning Power and Natural Gas Systems with Natural Gas Storage

The interdependency between power and natural gas is so tight, especially where natural gas extraction is economical. Therefore, co-expansion planning is imperative for having efficient systems with minimum cost. In this paper, multistage stochastic co-expansion planning power and natural gas systems is presented. Natural gas load flow (NGLF) is modeled with the Weymouth equation, a non-linear and non-convex problem. In order to overcome the non-convexity of the problem, mixed-integer second-order cone programming (MISOCP) is utilized to solve NGLF. Furthermore, linepack constraints are added to exploit the natural gas stored in the pipeline for co-expansion planning, mainly at the transmission level where voluminous pipelines are used and linepack is noticeable. Natural gas storage is considered in the model to alleviate operational and investment costs. Decreasing the investment and operational costs of co-expansion planning is the objective of the model. Investment decisions can be taken more than once so that investment costs can be divided into the whole planning horizon to avoid an enormous budget at the beginning of the planning horizon. Power and natural gas load growth are taken into account as long-term uncertainties. The proposed model is applied in a real case of southwestern Iran. The results determine that by implementing the proposed model, the investment and operational costs decrease 6.3% and 14%, respectively.