Due to computational restrictions, energy-system optimization models (ESOMs) and generation expansion planning models (GEPMs) frequently represent intraannual variations in demand and supply by using the data of a limited number of representative historical days. The vast majority of the current approaches to select a representative set of days relies on either simple heuristics or clustering algorithms and comparison of different approaches is restricted to different clustering algorithms. This paper contributes by: i) proposing criteria and metrics for evaluating representativeness, ii) providing a novel optimization-based approach to select a representative set of days, and iii) evaluating and comparing the developed approach to multiple approaches available from the literature. The developed optimization-based approach is shown to achieve more accurate results than the approaches available from the literature. As a consequence, by applying this approach to select a representative set of days, the accuracy of ESOMs/GEPMs can be improved without increasing the computational cost. The main disadvantage is that the approach is computationally costly and requires an implementation effort.

Renewable electricity generation not only provides affordable and emission-free electricity but also introduces additional complexity in the day-ahead planning procedure. To address the stochastic nature of renewable generation, system operators must schedule enough controllable generation to have the flexibility required to compensate unavoidable real-time mismatches between the production and consumption of electricity. This flexibility must be scheduled ahead of real-time and comes at a cost, which should be minimized without compromising the operational reliability of the system. Energy storage facilities, such as pumped hydro energy storage (PHES), can respond quickly to mismatches between demand and generation. Hydraulic constraints on the operation of PHES must be taken into account in the day-ahead scheduling problem, which is typically not done in deterministic models. Stochastic optimization enhances the procurement of flexibility, but requires more computational resources than conventional deterministic optimization. This paper proposes a deterministic and an interval unit commitment formulation for the co-optimization of controllable generation and PHES, including a representation of the hydraulic constraints of the PHES. The proposed unit commitment (UC) models are tested against a stochastic UC formulation on a model of the Belgian power system to compare the resulting operational cost, reliability, and computational requirements. The cost-effective regulating capabilities offered by the PHES yield significant operational cost reductions in both models, while the increase in calculation times is limited.

As the share of wind power in the electricity system rises, the limited predictability of wind power generation becomes increasingly critical for operating a power system reliably. In most operational and economic models, the wind power forecast error (WPFE) is often assumed to follow a Gaussian or the so-called β-distribution. However, these distributions might not be suited to fully describe the skewed and heavy-tailed character of WPFE data. In this paper, the Lévy α-stable distribution is proposed as an improved description of the WPFE. The method presented allows us to quantify the probability of a certain error, given a certain wind power forecast. Based on recent historical wind power data, the feasibility of the Lévy α-stable distribution as a WPFE description is demonstrated. The added value of this improved statistical model of the WPFE is illustrated in a state-of-the-art probabilistic reserve sizing method. Results show that this new statistical description of the WPFE can hold important information for short-term economic and operational (reliability) studies for power systems with a significant wind power penetration.