Emrah Öztürk | Searcharxiv

arXiv2024

Towards Efficient Aggregation of Storage Flexibilities in Power Grids

The increasing penetration of volatile renewables combined with increasing demands poses a challenge to modern power grids. Furthermore, distributed energy resources and flexible devices (electric vehicles, PV generation, ...) are becoming more widespread, making their aggregate usage for ancillary services interesting. However, accurately quantifying the aggregate flexibility of numerous flexible devices is known to be limited by the curse of dimensionality, i.e., it does not scale well computationally. This has led to the development of various approximation algorithms. In this study, we improve upon our previously proposed vertex-based inner approximation, extending it to more general storage devices. We demonstrate the efficacy and accuracy of the proposed method in a case study comparing our approach with an exact centralized control framework, where the flexibility of numerous electric vehicles is combined to reduce the peak load in a residential area.

math.OC↗

arXiv2024

Alleviating the Curse of Dimensionality in Minkowski Sum Approximations of Storage Flexibility

Many real-world applications require the joint optimization of a large number of flexible devices over time. The flexibility of, e.g., multiple batteries, thermostatically controlled loads, or electric vehicles can be used to support grid operation and to reduce operation costs. Using piecewise constant power values, the flexibility of each device over $d$ time periods can be described as a polytopic subset in power space. The aggregated flexibility is given by the Minkowski sum of these polytopes. As the computation of Minkowski sums is in general demanding, several approximations have been proposed in the literature. Yet, their application potential is often objective-dependent and limited by the curse of dimensionality. We show that up to $2^d$ vertices of each polytope can be computed efficiently and that the convex hull of their sums provides a computationally efficient inner approximation of the Minkowski sum. Via an extensive simulation study, we illustrate that our approach outperforms ten state-of-the-art inner approximations in terms of computational complexity and accuracy for different objectives. Moreover, we propose an efficient disaggregation method applicable to any vertex-based approximation. The proposed methods provide an efficient means to aggregate and to disaggregate energy storages in quarter-hourly periods over an entire day with reasonable accuracy for aggregated cost and for peak power optimization.

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