Scenario construction and reduction applied to stochastic power generation expansion planning

Abstract

A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone. Abstract:A challenging aspect of applying stochastic programming in a dynamic setting is to construct a set of discrete scenarios that well represents multivariate stochastic processes for uncertain parameters. Often this is done by generating a scenario tree using a statistical procedure and then reducing its size while maintaining its statistical properties. In this paper, we test a new scenario reduction heuristic in the context of long-term power generation expansion planning. We generate two different sets of scenarios for future electricity demands and fuel prices by statistical extrapolation of long-term historical trends. The cardinality of the first set is controlled by employing increasing length time periods in a tree structure while that of the second set is limited by its lattice structure with periods of equal length. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the widely-used forward selection heuristic for scenario reduction, we customize a new heuristic scenario reduction method named forward selection in wait-and-see clusters (FSWC) for this application. In this method, we first cluster the scenarios based on their wait-and-see solutions and then apply fast forward selection within clusters. Numerical results for a twenty year generation expansion planning case study indicate substantial computational savings to achieve similar solutions as those obtained by forward selection alone.

Application of scenario reduction to LDC and risk based generation expansion planning

“…Their constraints consist of ensuring that system demand is met in each period by the available generation capacity and limiting the number of certain generator types installed. Unlike the FSWC method presented in [14], which summarizes first stage decisions in terms of the cumulative numbers of generators of each type, the revised FSWC method in this paper includes a more detailed description of the differences between different expansion strategies. Based on these differences, impacts of different scenarios on expansion strategy are recognized more clearly than before, and thus better clusters and scenario subsets are identified.…”

“…However, reference [14] accounts only for yearly electricity demand, ignoring the variation in load levels in each year, and does not consider the investment risk associated with a long planning horizon. In this paper, we divide years into subperiods according to the load duration curve (LDC).…”

“…We choose a tree structure in this paper because the size of a tree can be controlled by its structure [2]. According to the approach mentioned in [14], scenarios are generated by making use of a moment matching method incorporating GBM processes.…”

“…In addition, there is no guarantee that the solutions obtained by their heuristic methods are optimal. To achieve a more reliable expansion strategy minimizing expected total cost, we use a scenario based two-stage stochastic GEP model [14]. The FSWC heuristic scenario reduction method is applied in [14] to mitigate the computational burden after scenario generation by incorporating GBM process and moment matching method.…”

Data-driven multi-stage scenario tree generation via statistical property and distribution matching

“…The intuitive idea is to find a subset of the original set of scenarios of prescribed cardinality that has the shortest distance to the remaining scenarios. Feng & Ryan (2013) modified that method to also account for what the authors call "key" first-stage decisions in the aggregation of scenarios in addition to probability metrics.…”