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Connecting Representative Periods in Energy System Optimization Models using Markov-Matrices

Felix C. A. Auer, Diego A. Tejada-Arango, Sonja Wogrin

TL;DR

The paper addresses the loss of temporal dynamics in time-series aggregation for energy-system optimization by introducing a Markov-Matrices framework that links representative periods (RPs) through data-driven transition probabilities $PR_{rp',rp}$ and expected-step substitutions. This approach extends to constraints that connect multiple time steps and to storage-related formulations, while accommodating a binary-relaxation strategy to preserve feasibility. Across illustrative and realistic (NREL-118) case studies, Markov Transition yields closer objective values, substantially reduces boundary-related errors, and maintains a modest computational footprint, with improvements scaling with the number of RPs. Overall, the method enhances chronological consistency in RP-based optimization, offering a scalable alternative to traditional edge-connections, particularly for systems with time-linked constraints at RP boundaries.

Abstract

Time series aggregation is a common approach to reduce the computational complexity of large-scale energy system optimization models. However, maintaining chronological continuity between the resulting representative periods (RPs) remains a key challenge, as transitions between RPs are typically lost. This leads to inaccuracies in storage behavior, unit commitment, and other time-linked aspects of the model. We propose a novel method that uses Markov-Matrices to link RPs via probabilistic transitions and expected values. The approach is also suitable for constraints that connect multiple time steps, and can be adjusted to work with binary variables. Benefits are shown on an illustrative case study and validated using the NREL-118 bus system, where it reduces the error to one fifth of the current state-of-the-art while retaining low computational complexity.

Connecting Representative Periods in Energy System Optimization Models using Markov-Matrices

TL;DR

The paper addresses the loss of temporal dynamics in time-series aggregation for energy-system optimization by introducing a Markov-Matrices framework that links representative periods (RPs) through data-driven transition probabilities and expected-step substitutions. This approach extends to constraints that connect multiple time steps and to storage-related formulations, while accommodating a binary-relaxation strategy to preserve feasibility. Across illustrative and realistic (NREL-118) case studies, Markov Transition yields closer objective values, substantially reduces boundary-related errors, and maintains a modest computational footprint, with improvements scaling with the number of RPs. Overall, the method enhances chronological consistency in RP-based optimization, offering a scalable alternative to traditional edge-connections, particularly for systems with time-linked constraints at RP boundaries.

Abstract

Time series aggregation is a common approach to reduce the computational complexity of large-scale energy system optimization models. However, maintaining chronological continuity between the resulting representative periods (RPs) remains a key challenge, as transitions between RPs are typically lost. This leads to inaccuracies in storage behavior, unit commitment, and other time-linked aspects of the model. We propose a novel method that uses Markov-Matrices to link RPs via probabilistic transitions and expected values. The approach is also suitable for constraints that connect multiple time steps, and can be adjusted to work with binary variables. Benefits are shown on an illustrative case study and validated using the NREL-118 bus system, where it reduces the error to one fifth of the current state-of-the-art while retaining low computational complexity.
Paper Structure (9 sections, 7 equations, 2 figures, 1 table)

This paper contains 9 sections, 7 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Transitions between Representative Periods
  3. Using Markov-Matrices
  4. Connecting Multiple Time Steps
  5. Dealing with Binary Variables
  6. Case Studies
  7. Illustrative Case Study
  8. Realistic Case Study
  9. Conclusion

Figures (2)

  • Figure 1: Illustration of a Transition Period $rp_1$ where the theoretically optimal $p$ can not be obtained due to a Cyclic Connection of the Ramp-Up constraint.
  • Figure 2: Solutions for illustrative case. Each plot in the top half shows demand, production, power-not-served (PNS) and excess-power-served (EPS), and in the bottom half the binary decisions of commitment, startup and shutdown.