Mathematical programming is frequently used to analyze the effect of implementing various climate and energy policies through the implementation of energy system investment models. A common feature of these models is a co-optimization of investments and system operation. Often perfect foresight is assumed, and sensitivity analysis then used for exploring the uncertainty. However, to construct solutions robust to the uncertainty stochastic programming (SP) is the method of choice. In the case of investment decisions there are uncertainties present at different time-scales. In a power system, for instance, investments in generation capacity are done under uncertainty, about short-term operating conditions (load, prices, intermittent production), but also about long-term developments (fuel prices, demand growth, policy regulation). Representing all the uncertainty in a single multi-stage tree will quickly produce an intractable problem, but there is a way to cast the problem such that it does not immediately explode in size. By making the assumption that observing realizations of short-term operational uncertainty does not provide updated information about future uncertainty (both short-term and long-term) the operational decisions in one stage of the tree can be decoupled from decisions in the following stages. The resulting tree then have two types of nodes, strategic nodes (representing investment stages) which are affected by future uncertainty, and operational nodes which are not. This greatly reduces the size of the problem and is the essence of multi-horizon tree formulation in stochastic programming. Multi-horizon trees are used in the SP models EMPIRE (capacity expansion model of the European power system) and RAMONA (gas infrastructure model) at the Norwegian University of Science and Technology. Joint work with Asgeir Tomasgard.
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