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N. Choudhary
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Real Worst-Case Period Selection in Time Series Aggregation for Energy System Planning
An Experimental Comparison Using the Tulipa Energy Model
Large-scale energy system planning requires solving capacity expansion problems
over complete hourly time series, which is computationally intractable. Selecting a
small set of representative periods compresses the input, but standard clustering meth-
ods miss rare extreme events and smooth over many local peaks, producing investment
plans that underestimate the true optimal cost. A construction from Elgersma [5]
addresses this by building an artificial worst-case period, but the result can be more
extreme than any historically observed day. This work investigates whether selecting a
real observed period to represent the worst case can match this quality while preserv-
ing the temporal coherence of each selected day, meaning its demand and availability
values reflect conditions that genuinely occurred together in the same 24-hour window.
Three real-period selection strategies are proposed and compared against two artifi-
cial worst-case variants and the standard k-medoids baseline using the Tulipa Energy
Model [4]. All non-fractional methods approach near-zero regret by approximately
k = 400 periods; no single method is consistently fastest, and the differences between
methods become negligible beyond that point. No real worst-case method consistently
improves reliability over plain k-medoids, but this result is explained by a dataset cal-
ibration issue rather than a fundamental failure of the approach. Two lessons emerge
regardless of the dataset: global weight scaling in the fractional-weight variant intro-
duces a persistent non-zero regret plateau that cannot be corrected by adding more
periods, and model-guided period selection doubles computation cost without benefit
when the planning model is not sensitive to reliability shortfalls. The weight-scaling
issue is structural, and the computational cost of the model-guided method follows
directly from its two-solve design. A realistically calibrated dataset is still needed to
fully evaluate the reliability benefit of real worst-case selection. ...
over complete hourly time series, which is computationally intractable. Selecting a
small set of representative periods compresses the input, but standard clustering meth-
ods miss rare extreme events and smooth over many local peaks, producing investment
plans that underestimate the true optimal cost. A construction from Elgersma [5]
addresses this by building an artificial worst-case period, but the result can be more
extreme than any historically observed day. This work investigates whether selecting a
real observed period to represent the worst case can match this quality while preserv-
ing the temporal coherence of each selected day, meaning its demand and availability
values reflect conditions that genuinely occurred together in the same 24-hour window.
Three real-period selection strategies are proposed and compared against two artifi-
cial worst-case variants and the standard k-medoids baseline using the Tulipa Energy
Model [4]. All non-fractional methods approach near-zero regret by approximately
k = 400 periods; no single method is consistently fastest, and the differences between
methods become negligible beyond that point. No real worst-case method consistently
improves reliability over plain k-medoids, but this result is explained by a dataset cal-
ibration issue rather than a fundamental failure of the approach. Two lessons emerge
regardless of the dataset: global weight scaling in the fractional-weight variant intro-
duces a persistent non-zero regret plateau that cannot be corrected by adding more
periods, and model-guided period selection doubles computation cost without benefit
when the planning model is not sensitive to reliability shortfalls. The weight-scaling
issue is structural, and the computational cost of the model-guided method follows
directly from its two-solve design. A realistically calibrated dataset is still needed to
fully evaluate the reliability benefit of real worst-case selection. ...
Large-scale energy system planning requires solving capacity expansion problems
over complete hourly time series, which is computationally intractable. Selecting a
small set of representative periods compresses the input, but standard clustering meth-
ods miss rare extreme events and smooth over many local peaks, producing investment
plans that underestimate the true optimal cost. A construction from Elgersma [5]
addresses this by building an artificial worst-case period, but the result can be more
extreme than any historically observed day. This work investigates whether selecting a
real observed period to represent the worst case can match this quality while preserv-
ing the temporal coherence of each selected day, meaning its demand and availability
values reflect conditions that genuinely occurred together in the same 24-hour window.
Three real-period selection strategies are proposed and compared against two artifi-
cial worst-case variants and the standard k-medoids baseline using the Tulipa Energy
Model [4]. All non-fractional methods approach near-zero regret by approximately
k = 400 periods; no single method is consistently fastest, and the differences between
methods become negligible beyond that point. No real worst-case method consistently
improves reliability over plain k-medoids, but this result is explained by a dataset cal-
ibration issue rather than a fundamental failure of the approach. Two lessons emerge
regardless of the dataset: global weight scaling in the fractional-weight variant intro-
duces a persistent non-zero regret plateau that cannot be corrected by adding more
periods, and model-guided period selection doubles computation cost without benefit
when the planning model is not sensitive to reliability shortfalls. The weight-scaling
issue is structural, and the computational cost of the model-guided method follows
directly from its two-solve design. A realistically calibrated dataset is still needed to
fully evaluate the reliability benefit of real worst-case selection.
over complete hourly time series, which is computationally intractable. Selecting a
small set of representative periods compresses the input, but standard clustering meth-
ods miss rare extreme events and smooth over many local peaks, producing investment
plans that underestimate the true optimal cost. A construction from Elgersma [5]
addresses this by building an artificial worst-case period, but the result can be more
extreme than any historically observed day. This work investigates whether selecting a
real observed period to represent the worst case can match this quality while preserv-
ing the temporal coherence of each selected day, meaning its demand and availability
values reflect conditions that genuinely occurred together in the same 24-hour window.
Three real-period selection strategies are proposed and compared against two artifi-
cial worst-case variants and the standard k-medoids baseline using the Tulipa Energy
Model [4]. All non-fractional methods approach near-zero regret by approximately
k = 400 periods; no single method is consistently fastest, and the differences between
methods become negligible beyond that point. No real worst-case method consistently
improves reliability over plain k-medoids, but this result is explained by a dataset cal-
ibration issue rather than a fundamental failure of the approach. Two lessons emerge
regardless of the dataset: global weight scaling in the fractional-weight variant intro-
duces a persistent non-zero regret plateau that cannot be corrected by adding more
periods, and model-guided period selection doubles computation cost without benefit
when the planning model is not sensitive to reliability shortfalls. The weight-scaling
issue is structural, and the computational cost of the model-guided method follows
directly from its two-solve design. A realistically calibrated dataset is still needed to
fully evaluate the reliability benefit of real worst-case selection.