What Are We Clustering For? Establishing Performance Guarantees for Time Series Aggregation in Generation Expansion Planning
Luca Santosuosso, Bettina Klinz, Sonja Wogrin
TL;DR
This work tackles generation expansion planning (GEP) under storage and time-coupled dynamics by introducing a time series aggregation (TSA) method with rigorous performance guarantees. It proves that aggregated MILP and MIQP GEP models provide valid lower bounds on the full-scale optimal value, independent of clustering technique, and it develops a TSA-based algorithm that iteratively refines objective-function bounds while delivering feasible full-scale solutions at each step (with bounds expressed as $\hat{J}(\hat{z}^{*}) \le J(z^{*})$ and $\hat{\bar{J}}(\hat{\bar{z}}^{*}) \le \bar{J}(\bar{z}^{*})$). The approach is benchmarked against full-scale optimization and Benders decomposition, showing substantial computational gains and restored tractability for MIQP instances, while enabling extension of bounds to stakeholder-specific metrics. The framework is demonstrated on high-renewables scenarios and is adaptable to other capacity-expansion problems, providing practical guidance for investment and operation under uncertainty. Overall, the study offers a robust, clustering-agnostic pathway to guaranteed performance in TSA-enhanced GEP and related domains.
Abstract
Generation expansion planning (GEP) is a prominent example of capacity expansion problems in operations research. Being generally NP-hard, GEP optimization models can become intractable when nonconvex dynamics, time-coupling constraints, and complex asset interactions are involved. Time series aggregation (TSA) tackles this by reducing temporal complexity via input data clustering. However, existing TSA methods either focus solely on preserving the statistical features of the input data, yielding heuristics without guarantees on the aggregated model's accuracy, or provide error bounds limited to linear models, neglecting time-coupling constraints and applying only to specific clustering techniques. Moreover, these bounds typically pertain solely to the GEP objective function and do not extend to other stakeholder-specific metrics, such as decision vector partitions. To tackle these issues, we demonstrate that an appropriately constructed aggregated model always provides a lower bound on the optimal objective function value of the full-scale GEP model in both mixed-integer linear and mixed-integer quadratic formulations with time-coupling, independent of the clustering technique employed. Building on this, we propose a performance-guaranteed TSA-based solution algorithm that iteratively refines objective function bounds while generating feasible solutions to the full-scale model at each iteration. We then discuss a comparison with Benders decomposition and demonstrate how the derived bounds can be extended to error estimates for stakeholder-specific metrics. Numerical results show the computational advantages of our method over both full-scale optimization and classical Benders decomposition.