A mean-variance approach to transmission network planning

We propose a two-attribute procedure for selecting the most cost-effective transmission expansion alternative under risk. The procedure randomly generates sets of realization of random parameters of the problem and for each set an optimization model that considers potential expansion options is solved. The mean and variance of the objective function associated with each optimal solution are the selection attributes. The optimal solution that has the smallest mean and variance is deemed the best expansion alternative. The procedure guarantees the selected best alternative is indeed the best by a probability that satisfies or exceeds a user's specified probability of correct selection. For numerical examples of this paper, the levels of load and generation, and availability of generators and lines are considered random variables. Numerical examples are used to demonstrate the advantages of the proposed selection criterion over using the traditional expected value selection criterion.