Efficient Vertex-Based Approximation for Energy Storage Flexibility

Core Concepts

The author proposes an efficient method for aggregating and disaggregating energy storages using vertex-based approximations, outperforming existing methods in terms of computational complexity and accuracy.

Abstract

The paper introduces a novel approach for efficiently handling the joint optimization of flexible devices over time. By computing vertices efficiently, the proposed method provides accurate inner approximations of Minkowski sums. The study showcases superior performance compared to state-of-the-art methods in terms of computational complexity and precision across various objectives. Additionally, an innovative disaggregation technique is presented, offering a means to distribute power profiles among individual devices effectively.

The research addresses the challenges posed by high-dimensional spaces in optimizing energy storage flexibility. By leveraging vertex-based approximations, the proposed method demonstrates significant improvements in computational efficiency and accuracy for cost and peak power optimization. The study also highlights the importance of efficient aggregation and disaggregation strategies in managing energy resources effectively.

Key points include:

• Real-world applications necessitate joint optimization of flexible devices.
• Proposed method computes vertices efficiently for accurate inner approximations.
• Outperforms existing approaches in terms of computational complexity and accuracy.
• Introduces an innovative disaggregation method for distributing power profiles effectively.

Stats

As the computation of Minkowski sums is demanding, several approximations have been proposed in the literature.
Up to 2d vertices of each polytope can be computed efficiently.
The proposed approach outperforms ten state-of-the-art inner approximations in terms of computational complexity and accuracy.

Quotes

"The proposed methods provide an efficient means to aggregate and to disaggregate energy storages."
"Our approach aims to compute certain vectors of extreme actions within the polytopes."

Key Insights Distilled From

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

by Emra... at arxiv.org 02-29-2024

https://arxiv.org/pdf/2311.01614.pdf

Deeper Inquiries

How does the proposed method compare with distributed optimization techniques

The proposed method for vertex-based approximation in aggregating and disaggregating energy storages differs from distributed optimization techniques in several ways. Distributed optimization methods typically involve decentralized decision-making processes where individual devices optimize their actions based on local information and constraints, aiming to achieve a global objective through coordination. On the other hand, the proposed method focuses on efficiently computing inner approximations of the Minkowski sum by leveraging vertices of polytopes representing flexible devices' capabilities.
While distributed optimization approaches can offer scalability and robustness in handling large-scale systems with multiple decision-makers, they often require communication among devices and may face challenges related to convergence and coordination. In contrast, the vertex-based approximation method provides a computationally efficient means to aggregate flexibility without necessitating extensive communication or iterative optimization procedures across devices.
In summary, the proposed vertex-based approach offers a more streamlined and computationally efficient way to approximate aggregated flexibility compared to traditional distributed optimization techniques.

What are the implications of Assumption 2 not being satisfied for energy storages

If Assumption 2 is not satisfied for energy storages represented by polytopes, it has significant implications for modeling and computation. Assumption 2 requires that if a vector x belongs to a polytope P(A,b), then all its projections onto lower-dimensional spaces must also belong to P(A,b). Additionally, it mandates that the zero vector (representing no use of flexibility) should be included in P(A,b).
When this assumption is violated for energy storages, it indicates that certain configurations or combinations of power values within the storage's feasible region do not align with expected behavior or constraints. This could lead to inaccuracies in aggregation results as well as potential inconsistencies when disaggregating aggregated profiles back into individual device-level actions.
Furthermore, violating Assumption 2 may result in computational challenges during aggregation due to non-feasible elements being considered or incorrect representations of collective flexibility. It underscores the importance of ensuring consistency across different dimensions when modeling flexible devices' capabilities.

How can vertex-based approximations be extended to handle non-polytopic sets like energy storages with charging efficiencies

To extend vertex-based approximations to handle non-polytopic sets like energy storages with charging efficiencies, one approach could involve incorporating additional parameters or constraints into the existing framework. For instance:

Efficiency Constraints: Integrate efficiency factors into the polytope representation by adjusting charging/discharging rates based on efficiency levels.

Time-Dependent Energy Constraints: Include time-varying constraints such as peak demand periods or off-peak pricing structures within each device's flexibility model.

Availability Restrictions: Account for limitations on device availability at specific times or under certain conditions by introducing binary variables indicating operational states.

Robust Optimization Techniques: Implement robust optimization methodologies considering uncertainties associated with efficiency variations or availability fluctuations.

By adapting vertex-based algorithms to accommodate these complexities inherent in real-world energy storage systems, researchers can enhance accuracy and applicability while addressing practical considerations essential for effective deployment in smart grid environments."