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Accurately modeling long-term storage with minimum representative hours in large-scale renewable energy systems

Jacob Mannhardt, Lukas Kunz, Giovanni Sansavini

TL;DR

The paper tackles the challenge of accurately modeling long-term storage within time-series aggregated energy system optimization models. It introduces a reduced representative-hours (RH) storage representation that clusters RH inputs while reconstructing storage evolution with far fewer variables, marrying RH accuracy with RD-like computational efficiency. Benchmarking against representative days (RD), RH, and chronological RH (CRH) on a net-zero European energy system demonstrates dramatic solving-time reductions with minimal objective-value error (around 7–11%) at moderate to strong aggregations (roughly 100–500 RH). The approach is robust across multiple model variants and is implemented in the open-source ZEN-garden platform, making it practically valuable for large-scale, sector-coupled energy system analyses.

Abstract

Energy system optimization often relies on time series aggregation to ensure computational tractability. Aggregation generally loses the chronology of time steps, which renders the storage level representation challenging. Typically, this challenge is addressed by using representative days (RD) to utilize intra-day chronology, even though representative hours (RH) can describe the input time series more accurately at fewer representative time steps than RD. However, until now, the use of RH storage representation methods has been limited by either high computational complexity, poor accuracy in clustering and storage representation, or restricted applicability. Here, we present a novel storage representation method based on RH that combines the high accuracy of RH time series aggregation with the high computational efficiency of methods based on RD. Through benchmarking the four most established storage representation methods on a model of a net-zero European energy system, we find that the proposed method can reduce the solving time by over 95% for the same objective value compared to the most established RD and RH methods. The proposed method exhibits particular strengths at strong aggregations of around 100 to 500 representative hours per year, making the method especially applicable to large-scale and sector-coupled transition pathway models. The developed method for accurately modeling both short-term and long-term storage, along with the presented findings, is of practical relevance to energy system modelers who seek computational tractability in large-scale applications while avoiding the misallocation of storage and conversion capacities.

Accurately modeling long-term storage with minimum representative hours in large-scale renewable energy systems

TL;DR

The paper tackles the challenge of accurately modeling long-term storage within time-series aggregated energy system optimization models. It introduces a reduced representative-hours (RH) storage representation that clusters RH inputs while reconstructing storage evolution with far fewer variables, marrying RH accuracy with RD-like computational efficiency. Benchmarking against representative days (RD), RH, and chronological RH (CRH) on a net-zero European energy system demonstrates dramatic solving-time reductions with minimal objective-value error (around 7–11%) at moderate to strong aggregations (roughly 100–500 RH). The approach is robust across multiple model variants and is implemented in the open-source ZEN-garden platform, making it practically valuable for large-scale, sector-coupled energy system analyses.

Abstract

Energy system optimization often relies on time series aggregation to ensure computational tractability. Aggregation generally loses the chronology of time steps, which renders the storage level representation challenging. Typically, this challenge is addressed by using representative days (RD) to utilize intra-day chronology, even though representative hours (RH) can describe the input time series more accurately at fewer representative time steps than RD. However, until now, the use of RH storage representation methods has been limited by either high computational complexity, poor accuracy in clustering and storage representation, or restricted applicability. Here, we present a novel storage representation method based on RH that combines the high accuracy of RH time series aggregation with the high computational efficiency of methods based on RD. Through benchmarking the four most established storage representation methods on a model of a net-zero European energy system, we find that the proposed method can reduce the solving time by over 95% for the same objective value compared to the most established RD and RH methods. The proposed method exhibits particular strengths at strong aggregations of around 100 to 500 representative hours per year, making the method especially applicable to large-scale and sector-coupled transition pathway models. The developed method for accurately modeling both short-term and long-term storage, along with the presented findings, is of practical relevance to energy system modelers who seek computational tractability in large-scale applications while avoiding the misallocation of storage and conversion capacities.

Paper Structure

This paper contains 22 sections, 24 equations, 13 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Storage representation in time-aggregated ESOMs - A short review
  3. Methods
  4. Clustering representative days and representative hours
  5. Proposed reduced RH storage representation
  6. Case study of a net-zero European electricity and heating system
  7. Results
  8. Objective value versus solving time
  9. Approximation accuracy of conversion and storage capacities
  10. Robustness of methods for various large-scale energy system models
  11. Discussion
  12. Conclusions
  13. Mathematical description of benchmarked storage representation methods
  14. Storage representation approaches for representative days
  15. Superposition, hourly storage level limit constraint
  16. ...and 7 more sections

Figures (13)

  • Figure 1: Schematic depiction of the time series aggregation (blue) and storage level representation (green) approaches with representative hours (RH). The fictional fully resolved time series (grey) is aggregated to 8 representative hours (numbers underneath the left plot). The storage level is represented with the presented reduced RH storage representation method for the storage level time steps (numbers underneath the right plot).
  • Figure 2: Solving time versus relative objective error for the five investigated storage representation methods. Every method is repeated five times for each time step configuration. The error bar indicates the 95% confidence interval in solving time. Note that the y-axis is shown logarithmically. The linear lines show an exponential regression of the mean solving time and objective value.
  • Figure 3: Disaggregated cost error for Proposed method (RH), Superposition (RD), and Chrono (CRH), relative to fully resolved total cost (326.3 bn Euro). Full storage resolution and MinMax are not shown, as they have the same system design as Proposed method and Superposition, respectively.
  • Figure 4: Relative error in electricity generation capacity for Superposition (RD), Proposed method (RH), and Chrono (CRH), relative to fully resolved capacities. The technologies are ranked by total capacity. Full storage resolution and MinMax are not shown, as they have the same system design as Proposed method and Superposition, respectively.
  • Figure 5: Relative error in electricity storage capacity for Superposition (RD), Proposed method (RH), and Chrono (CRH), relative to fully resolved capacities. The technologies are ranked by total capacity. Full storage resolution and MinMax are not shown, as they have the same system design as Proposed method and Superposition, respectively.
  • ...and 8 more figures