Optimal Selection of Sample Weeks for Approximating the Net Load in Generation Planning Problems

1 1 Abstract— The increasing presence of variable energy resources (VER) in power systems –most notably wind and solar power– demands tools capable of evaluating the flexibility needs to compensate for the resulting variability in the system. Capacity expansion models are needed that embed unit commitment decisions and constraints to account for the interaction between hourly variability and realistic operating constraints. However, the dimensionality of this problem grows proportionally with the time horizon of the load profile used to characterize the system, requiring massive amounts of computing resources. One possible solution to overcome this computational problem is to select a small number of representative weeks, but there is no consistent criterion to select these weeks, or to assess the validity of the approximation. This paper proposes a methodology to optimally select a given number of representative weeks that jointly characterize demand and VER output for capacity planning models aimed at evaluating flexibility needs. It also presents different measures to assess the error between the approximation and the complete time series. Finally, it demonstrates that the proposed methodology yields a valid approximation for unit commitment constraints embedded in long-term planning models. NOMENCLATURE í µí° ¶í µí°¹ í µí±— í µí±†í µí±‚í µí°¿í µí°´í µí±… Solar PV power capacity factor level at hour j í µí° ¶í µí°¹ í µí±— í µí±Ší µí°¼í µí±í µí°· Wind power capacity factor level at hour j í µí° ¶í µí°¹í µí°¸í µí±‹ Capacity factor error of technology X í µí°· í µí±— Demand level at hour j í µí°¸í µí° ¶í µí°¸í µí±‹ Energy contribution error of technology X í µí±— ∈ í µí°½ Index for the set of hours í µí°¿í µí°·í µí° ¶ Load duration curve í µí°¿í µí°·í µí° ¶ � Load duration curve approximation í µí±í µí°¿í µí°·í µí° ¶ Net load duration curve