In deregulated electricity markets, the electricity consumer should optimally divide the necessary electrical energy into different markets such as cash markets with spot prices and bilateral contract markets. This study aims to design a model to optimally select the electrical energy portfolio to minimize purchase costs by considering a risk level. For this purpose, an optimization model is proposed through the modern portfolio theory (MPT), mean-variance analysis, and conditional value-at-risk (CVaR) for cost minimization and risk reduction in the electricity supply problem. The mean-variance and CVaR were used as appropriate criteria for reducing unfavorable states in decision-making under uncertainty. Moreover, an artificial neural network was employed to predict the spot prices of the energy pool and the Iran Energy Exchange (IRENEX). The simulation was based on the actual data of Iran for 2018 and 2019. The entire statistical population was analyzed due to the small number of industrial subscribers, and the proposed model was implemented and executed in MATLAB software. Different sensitivity analyses proved the efficiency of the proposed models. According to the results, if an energy purchaser evades more risks, — i.e., the risk evasion coefficient increases a lower ratio of the electrical energy portfolio is allocated to cash markets, especially the IRENEX. In addition, the CVaR provided electricity markets with a more stable energy allocation than the mean-variance model