To account for volatile renewable energy supply, energy systems optimization problems require high temporal resolution. Many models use time-series clustering to find representative periods to reduce the amount of time-series input data and make the optimization problem computationally tractable. However, clustering methods remove peaks and other extreme events, which are important to achieve robust system designs. We present a general decision framework to include extreme events in a set of representative periods. We introduce a method to find extreme periods based on the slack variables of the optimization problem itself. Our method is evaluated and benchmarked with other extreme period inclusion methods from the literature for a design and operations optimization problem: a residential energy supply system. Our method ensures feasibility over the full input data of the residential energy supply system although the design optimization is performed on the reduced data set.
We show that using extreme periods as part of representative periods improves the accuracy of the optimization results by 3% to more than 75% depending on system constraints compared to results with clustering only, and thus reduces system cost and enhances system reliability.
Analysing the interactions between demand side and supply side investment decisions in an oligopolistic electricity market using a stochastic mixed complementarity problem
