Alleviating the Curse of Dimensionality in Minkowski Sum Approximations of Storage Flexibility
CoRR(2023)
摘要
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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