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Feedback Enhancement of Time Series Aggregation for Power System Expansion Planning

Ruiqi Zhang, Ensieh Sharifnia, Simon H. Tindemans

TL;DR

The paper tackles the intractability of high-resolution data in power system expansion planning by using time series aggregation (TSA) and reveals that purely statistical clustering can miss critical operating conditions. It derives bounds linking TSA operational accuracy to investment decisions and shows that operational errors are highly imbalanced across representative periods. To tighten the decision-bound gap, it introduces a feedback-enhanced TSA that iteratively identifies worst-performing representatives and re-clusters only their linked days, significantly improving both the decision error and the operational bound relative to mean-based clustering. A case study on the IEEE 24-bus RTE system demonstrates substantial gains in planning reliability and bound tightness, highlighting the method’s practical potential for balancing solution quality and computational effort.

Abstract

As a consequence of the high variability of load demand and renewable generation, long-term and high-resolution inputs are required for power system expansion planning, making the problem intractable in real-world applications. Time series aggregation (TSA), which captures representative patterns, reduces temporal complexity while providing similar planning outputs. However, purely statistical clustering, even when enhanced with predefined ``extremes'', can overlook system-specific critical operating conditions, making it unreliable across real-world systems. Therefore, this paper links TSA accuracy on specific system operation and final solution quality, which becomes a practical bound with mean-based TSA approaches. It is observed that the distribution of operational errors is highly imbalanced, such that a few representatives dominate the total error. This paper proposes an adaptive clustering strategy based on feedback enhancement of TSA that iteratively identifies poor-performing representatives with high operational error and re-clusters only their associated periods. A study shows that the feedback enhancement improves the decision error and tighten the bound significantly compared with the plain mean-based clustering method, offering a diagnostic for TSA quality, while balancing the computational effort with solution accuracy.

Feedback Enhancement of Time Series Aggregation for Power System Expansion Planning

TL;DR

The paper tackles the intractability of high-resolution data in power system expansion planning by using time series aggregation (TSA) and reveals that purely statistical clustering can miss critical operating conditions. It derives bounds linking TSA operational accuracy to investment decisions and shows that operational errors are highly imbalanced across representative periods. To tighten the decision-bound gap, it introduces a feedback-enhanced TSA that iteratively identifies worst-performing representatives and re-clusters only their linked days, significantly improving both the decision error and the operational bound relative to mean-based clustering. A case study on the IEEE 24-bus RTE system demonstrates substantial gains in planning reliability and bound tightness, highlighting the method’s practical potential for balancing solution quality and computational effort.

Abstract

As a consequence of the high variability of load demand and renewable generation, long-term and high-resolution inputs are required for power system expansion planning, making the problem intractable in real-world applications. Time series aggregation (TSA), which captures representative patterns, reduces temporal complexity while providing similar planning outputs. However, purely statistical clustering, even when enhanced with predefined ``extremes'', can overlook system-specific critical operating conditions, making it unreliable across real-world systems. Therefore, this paper links TSA accuracy on specific system operation and final solution quality, which becomes a practical bound with mean-based TSA approaches. It is observed that the distribution of operational errors is highly imbalanced, such that a few representatives dominate the total error. This paper proposes an adaptive clustering strategy based on feedback enhancement of TSA that iteratively identifies poor-performing representatives with high operational error and re-clusters only their associated periods. A study shows that the feedback enhancement improves the decision error and tighten the bound significantly compared with the plain mean-based clustering method, offering a diagnostic for TSA quality, while balancing the computational effort with solution accuracy.

Paper Structure

This paper contains 18 sections, 3 theorems, 21 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Error Analysis of Representative Periods in Power System Expansion Planning
  3. Expansion Planning with Representative Periods
  4. Performance Metrics of Representative Periods
  5. Simplification error (reduced vs. full optimum)
  6. Simplification error (reduced vs. full optimum)
  7. Decision error (true suboptimality of the estimated decision)
  8. Operational estimation error
  9. Linking Operational Performance to Planning Outcomes
  10. Practical Error Bound for Mean-based Aggregation
  11. Case Study: IEEE 24-bus RTE Test System
  12. Analysis of Operational Estimation Error
  13. Operational Estimation Error over Original Days
  14. Operational Estimation Error over Representative Days
  15. Feedback Enhancement of Time series Aggregation
  16. ...and 3 more sections

Key Result

Proposition 1

For any reduced set $\hat{\mathcal{D}}$ and corresponding optimal decision $\hat{x}$, its decision error is non-negative and upper-bounded by the difference of operational estimation errors for the actual optimal decision $x^\star$ and the estimated decision $\hat{x}$.

Figures (4)

  • Figure 1: Relationship between three optimization models: reduced-scale planning model; full-scale operational cost model; and the reference full-scale planning model.
  • Figure 2: Distribution of operational estimation error and time-series error across original days, for 20 and 40 RDs.
  • Figure 3: Distribution of operational estimation error across representative days, evaluated for the approximate solution $\hat{x}$ resulting from the use of RDs (blue) and the reference solution $x^\star$ (red).
  • Figure 4: Performance of reduced-scale planning model with different number of RDs using iterative re-clustering (starting from 20 and 30) and benchmarking with the direct mean-based hierarchical clustering method.

Theorems & Definitions (6)

  • Proposition 1: General Bound on Decision Error
  • proof
  • Proposition 2: Under-Estimation with Mean-based Clustering teichgraeber_clustering_2019li_representative_2022
  • proof
  • Theorem 1
  • proof