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

Two-stage stochastic mixed-integer programming models are formulated for minimizing expected cost or Conditional Value-at-Risk (CVaR) of a long-term power generation expansion planning problem incorporating load duration curves. The multivariate stochastic processes, such as electricity demands and fuel prices, are modeled as geometric Brownian motion (GBM) processes. Scenario paths for their future evolution are generated by statistical extrapolation of long-term historical trends. The size of the scenario set is controlled by using increasing length time periods in a tree structure. Nevertheless, some method of scenario thinning is necessary to achieve manageable solution times. To mitigate the computational complexity of the forward selection heuristic for scenario reduction, a combined heuristic scenario reduction method named Forward Selection in Wait-and-see Clusters (FSWC) is applied to the large scenario set. 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.