[Paper Review] Matrix Modeling of Energy Hub with Variable Energy Efficiencies

Wujing Huang, Ning Zhang+4 more|arXiv (Cornell University)|Apr 11, 2019

Integrated Energy Systems Optimization24 references4 citations

TL;DR

This paper proposes a matrix-based modeling approach for energy hubs with variable energy efficiencies by using piecewise linearization to transform nonlinear conversion and storage components into equivalent linear structures. The method enables automated, computer-aided modeling and optimization of multi-energy systems under variable efficiency conditions, improving both approximation accuracy and computational efficiency in operational planning.

ABSTRACT

The modeling of multi-energy systems (MES) is the basic task of analyzing energy systems integration. The variable energy efficiencies of the energy conversion and storage components in MES introduce nonlinearity to the model and thus complicate the analysis and optimization of MES. In this paper, we propose a standardized matrix modeling approach to automatically model MES with variable energy efficiencies based on the energy hub (EH) modeling framework. We use piecewise linearization to approximate the variable energy efficiencies; as a result, a component with variable efficiency is equivalent to several parallel components with constant efficiencies. The nonlinear energy conversion and storage relationship in EH can thus be further modeled under a linear modeling framework using matrices. Such matrix modeling approach makes the modeling of an arbitrary EH with nonlinear energy components highly automated by computers. The proposed modeling approach can further facilitate the operation and planning optimization of EH with variable efficiencies. Case studies are presented to show how the nonlinear approximation accuracy and calculation efficiency can be balanced using the proposed model in the optimal operation of EH.

Motivation & Objective

• To address the challenge of modeling multi-energy systems (MES) with nonlinear components due to variable energy efficiencies.
• To develop a standardized, automated modeling framework that simplifies the analysis and optimization of energy hubs (EHs).
• To enable linearization of nonlinear energy conversion and storage relationships through piecewise approximation.
• To improve computational efficiency and approximation accuracy in EH operation and planning optimization.

Proposed method

• The paper employs a matrix-based energy hub (EH) modeling framework to represent energy flows and conversions systematically.
• Variable energy efficiencies in conversion and storage components are approximated using piecewise linearization.
• Each component with variable efficiency is decomposed into multiple parallel components, each with a constant efficiency.
• The resulting model transforms the original nonlinear relationships into a linear matrix formulation, enabling efficient computation.
• The approach supports automated modeling via computer implementation, reducing manual modeling complexity.
• The method is validated through case studies focusing on balancing approximation accuracy and computational speed.

Experimental results

Research questions

• RQ1 How can variable energy efficiencies in energy conversion and storage components be effectively modeled in a linear framework?
• RQ2 To what extent can piecewise linearization accurately approximate nonlinear efficiency curves in energy hubs?
• RQ3 Can the proposed matrix modeling approach significantly improve computational efficiency in EH optimization?
• RQ4 How can the trade-off between approximation accuracy and computational cost be balanced in practical applications?

Key findings

• The proposed matrix modeling approach successfully transforms nonlinear energy hub components into a linear matrix framework, enabling automated modeling.
• Piecewise linearization allows accurate approximation of variable efficiency curves with minimal computational overhead.
• The method achieves a favorable balance between modeling accuracy and computational efficiency in case studies.
• The approach facilitates efficient operation and planning optimization of energy hubs with variable efficiencies.
• Case studies demonstrate that the model maintains high accuracy while reducing solution time compared to traditional nonlinear methods.
• The framework is scalable and adaptable to various energy hub configurations with complex nonlinear components.