Hybrid robust/stochastic transmission expansion planning considering uncertainties in generators’ offer prices: A second-order cone program approach

Abstract

The aim of this paper is to propose a hybrid robust/stochastic model for transmission expansion planning (TEP) problem. The uncertainties related to demand and wind are modelled via stochastic programming (SP), while the uncertainties associated with the generators’ offer prices are modelled via robust optimization (RO). In this sense, an ellipsoidal uncertainty set is considered which the offer price values are known to lie in these given ellipsoids. The model presented is then divided into a master problem and several independent subproblems using a tailored implementation of Bender's decomposition (BD) method. Robust linear constraints of the lower level problems are then transformed into a convex second-order cone programming (SOCP) problem. We will apply the proposed model to IEEE-118 bus power system showing that generators’ offer price and their correlation can considerably affect the optimal plan of the transmission planning. It is observed that considering correlation among generators’ offer prices would not necessarily yield more expensive expansion plan in comparison with the case where correlation is ignored. Indeed, increase or decrease in investment cost depends on the entries of the variance-covariance matrix, network topology and the location of generators. Moreover, the results show the computational efficiency of the robust convex model.