arXiv subjects

Karl Zhu

Publications and source records attributed to Karl Zhu.

3 recordsLinked to original sources

arXiv2026

Strike Price Optimization for ISO New England's Day-Ahead Ancillary Services

ISO New England's (ISO-NE) Day-Ahead Ancillary Services Initiative settles reserve products as financial call options on real-time energy prices. The system-wide strike price creates an efficiency-reliability tradeoff: increasing it lowers competitive reserve offers, but weakens resources' incentives to incur preparation costs and remain available for real-time performance. The existing strike price rule does not explicitly account for heterogeneous resource incentives and reserve requirements. We develop an optimization framework that selects the highest strike price while ensuring that enough resources retain an incentive to prepare and collectively satisfy the reserve requirements. Because a resource's preparation decision may affect the resulting real-time price distribution, its incentive depends on an unobservable counterfactual. To address this, we derive a tight lower-bound certificate using only the available conditional price distribution and a bound on the resource's price impact. We show that each resource enters the optimization through a single incentive threshold and that any finite optimal strike price occurs at one of these thresholds. This yields a tractable exact solution method based on threshold calculations and a small number of linear feasibility checks. Using reconstructed ISO-NE conditional price distributions and representative gas-fired resources, we find that higher heat-rate combustion turbines are more likely than combined-cycle resources to constrain the strike price choice.

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arXiv2026

Robust Optimization for Green Ammonia Production

The central challenge in optimizing green ammonia systems is satisfying the minimum-load requirements of the Haber-Bosch (HB) process under renewable uncertainty. We develop a robust optimization framework consisting of a strategic capacity planning model and an operational flow model under solar and wind uncertainty. The strategic model is a mixed-integer optimization (MIO) problem with flexible HB operating modes, namely hot-idling and shutdowns. To address the resulting computational challenges, we propose a robust scenario-reduction framework that combines k-means clustering with robust optimization to generate adversarial renewable trajectories. For the operational model, we develop adaptive robust rolling-horizon formulations under forecast uncertainty. Computational results show that the proposed framework produces feasible capacity plans under out-of-sample simulation, whereas existing approaches based on constraint aggregation fail to satisfy HB minimum-load requirements. Adaptive policies achieve higher ammonia production than static robust policies for a given robustness level, but provide weaker protection against realizations outside the uncertainty set.

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arXiv2025

Overfitting in Adaptive Robust Optimization

Adaptive robust optimization (ARO) extends static robust optimization by allowing decisions to depend on the realized uncertainty - weakly dominating static solutions within the modeled uncertainty set. However, ARO makes previous constraints that were independent of uncertainty now dependent, making it vulnerable to additional infeasibilities when realizations fall outside the uncertainty set. This phenomenon of adaptive policies being brittle is analogous to overfitting in machine learning. To mitigate against this, we propose assigning constraint-specific uncertainty set sizes, with harder constraints given stronger probabilistic guarantees. Interpreted through the overfitting lens, this acts as regularization: tighter guarantees shrink adaptive coefficients to ensure stability, while looser ones preserve useful flexibility. This view motivates a principled approach to designing uncertainty sets that balances robustness and adaptivity.

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