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@@ -53,12 +53,12 @@ hydrogen can be converted back into electricity (power-to-power),
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it can be used to produce low-carbon fuels (power-to-fuel),
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and it can be used to fuel hydrogen vehicles (power-to-mobility).
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The performance of these hydrogen-based energy systems is subject to uncertainties,
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such as the uncertainty on the solar irradiance, the energy consumption of hydrogen-powered buses and the price of grid electricity.
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such as the uncertainty on the solar irradiance, the energy consumption of hydrogen-powered buses, and the price of grid electricity.
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Disregarding these uncertainties in the design process can result in a drastic mismatch between simulated and real-world performance,
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and thus lead to a *kill-by-randomness* of the system.
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The *Robust design optimization of renewable Hydrogen and dErIved energy cArrier systems* (RHEIA) framework provides a robust design optimization pipeline
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that considers real-world uncertainties and yields robust designs, i.e., designs with a performance less sensitive to these uncertainties.
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Moreover, RHEIA includes models to evaluate hydrogen's techno-economic and environmental performance in a power-to-fuel, power-to-power and power-to-mobility context.
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Moreover, RHEIA includes models to evaluate hydrogen's techno-economic and environmental performance in a power-to-fuel, power-to-power, and power-to-mobility context.
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When combined, RHEIA unlocks the robust designs for hydrogen-based energy systems.
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As RHEIA considers the system models as a black box, the framework can be applied to existing open-source and closed-source models.
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To illustrate, an interface with the [EnergyPLAN](https://www.energyplan.eu/) software is included in the framework.
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Incorporating hydrogen is still an anomaly in design optimization studies of renewable energy systems [@Eriksson2017].
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Moreover, the optimization is often performed under the assumption of deterministic parameters (i.e., fixed, free from inherent variation).
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Considering fixed values for model parameters in design optimization yields designs that might be sensitive -- the real issue is that we cannot know-- to real-world uncertainties
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Considering fixed values for model parameters in design optimization yields designs that might be sensitive -- the real issue is that we cannot know -- to real-world uncertainties
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and results in a drastic mismatch between simulated and actual performances.
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In fields different from energy systems, e.g., structural mechanics, aerospace and automobile applications,
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Robust Design Optimization (RDO) yielded robust designs by minimizing the variance on the performance [@orosz2020robust].
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In fields different from energy systems, e.g., structural mechanics, aerospace, and automobile applications,
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Robust Design Optimization (RDO) yields robust designs by minimizing the variance on the performance [@orosz2020robust].
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Consequently, alternative design solutions were proposed that provide the least sensitive performance to the random environment.
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To ensure the computational tractability of RDO, surrogate modelling techniques achieve a promising computational efficiency
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to quantify the mean and variance on the performance. Nevertheless, applications of such surrogate-assisted robust design optimization techniques are limited [@Chatterjee2017].
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to quantify the mean and variance of the performance. Nevertheless, applications of such surrogate-assisted robust design optimization techniques are limited [@Chatterjee2017].
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To fill these research gaps, RHEIA provides a multi-objective RDO algorithm,
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for which the uncertainty quantification is performed through a Polynomial Chaos Expansion (PCE) surrogate modelling technique.
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In addition, RHEIA includes Python-based models for relevant valorization pathways of hydrogen: power-to-fuel, power-to-power and power-to-mobility.
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In addition, RHEIA includes Python-based models for relevant valorization pathways of hydrogen: power-to-fuel, power-to-power, and power-to-mobility.
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The significant techno-economic and environmental uncertainties for these models are characterized based on scientific literature,
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and a method is included to gather climate data and demand data for the location of interest.
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Finally, RHEIA allows connecting your own models to the RDO and uncertainty quantification algorithms as well.
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Simulation models that include the evaluation of hydrogen-based energy systems exist,
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e.g., [INSEL](https://insel.eu/en/home_en.html), [EnergyPLAN](https://www.energyplan.eu/) and [TRNSYS](http://www.trnsys.com/).
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e.g., [INSEL](https://insel.eu/en/home_en.html), [EnergyPLAN](https://www.energyplan.eu/), and [TRNSYS](http://www.trnsys.com/).
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Despite their extensive component model libraries, these simulation models lack an optimization feature.
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[HOMER Energy](https://www.homerenergy.com/products/pro/index.html) includes an optimization algorithm to design hybrid microgrids, including hydrogen system component models.
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In Python, [Calliope](https://www.callio.pe/) [@pfenninger2018calliope] considers the optimization of multi-scale energy system models, where hydrogen is regarded as a fuel in advanced gas turbines.
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The first author acknowledges the support from the Belgian federal Energy Transition Fund, project DRIVER.
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# References
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# References

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