A comparison of stochastic and adaptation programming methods for long term generation and transmission co-optimization under uncertainty

In this work a recently developed mathematical programming formulation called adaptation is compared with the widely used stochastic programming method in the context of electric infrastructure expansion planning. Although the structure of the adaptation method closely resembles that of a generic stochastic program it diverges from the temporal conventions of traditional electric infrastructure formulations. While traditional stochastic programming formulations restrict first and later stage capacity investments to separate time periods, the first and later stage capacity investments in adaptation overlap in time. Additionally, recourse decisions for all scenarios are defined relative to the central core trajectory in the same time period rather than the node at the previous time period in the stochastic programming scenario tree. After an in-depth discussion of stochastic programming and adaptations' formulations, a six bus simulation is provided to facilitate a more concrete comparison of the two methods. Uncertainties considered in the simulation include, wind and solar build costs, carbon taxes, demand and peak demand growth, natural gas fuel prices, and transmission costs.