[Paper Review] Modeling Time-dependent CO$_2$ Intensities in Multi-modal Energy Systems with Storage

Christopher Ripp, Florian Steinke|arXiv (Cornell University)|Jun 11, 2018

Integrated Energy Systems Optimization12 references3 citations

TL;DR

This paper proposes two novel methods for computing time-dependent CO₂ intensities in multi-modal energy systems with storage: an 'as-is' analysis that traces actual emissions across all energy flows, and a 'what-if' analysis that computes marginal emission changes from infinitesimal demand shifts. The key contribution is an efficient computational method using linear programming sensitivities, enabling accurate, real-time CO₂ intensity tracking in complex, coupled energy systems with storage and sector coupling.

ABSTRACT

CO$_2$ emission reduction and increasing volatile renewable energy generation mandate stronger energy sector coupling and the use of energy storage. In such multi-modal energy systems, it is challenging to determine the effect of an individual player's consumption pattern onto overall CO$_2$ emissions. This, however, is often important to evaluate the suitability of local CO$_2$ reduction measures. Due to renewables' volatility, the traditional approach of using annual average CO$_2$ intensities per energy form is no longer accurate, but the time of consumption should be considered. Moreover, CO$_2$ intensities are highly coupled over time and different energy forms due to sector coupling and energy storage. We introduce and compare two novel methods for computing time-dependent CO$_2$ intensities, that address different objectives: the first method determines CO$_2$ intensities of the energy system as is. The second method analyzes how overall CO$_2$ emissions would change in response to infinitesimal demand changes. Given a digital twin of the energy system in form of a linear program, we show how to compute these sensitivities very efficiently. We present the results of both methods for two simulated test energy systems and discuss their different implications.

Motivation & Objective

• Address the limitations of annual average CO₂ intensities in high-renewable, multi-modal energy systems with storage and sector coupling.
• Provide a reliable method for assessing the true CO₂ impact of individual energy consumption or generation patterns in dynamic, coupled energy systems.
• Develop computationally efficient techniques to compute time-varying CO₂ intensities for practical deployment in energy system optimization and policy design.
• Resolve circular reasoning issues arising from interdependencies between energy forms and storage in multi-energy systems.
• Differentiate between two distinct but complementary approaches—'as-is' and 'what-if'—for CO₂ intensity computation based on different decision-making needs.

Proposed method

• Formulate the energy system as a linear program (LP) digital twin to represent all energy flows, conversions, and storage dynamics.
• Implement the 'as-is' analysis by computing CO₂ intensities as the ratio of total system emissions to energy output, tracing emissions across all processes and storage states.
• Implement the 'what-if' analysis using sensitivity analysis of the LP dual variables to compute the marginal change in total CO₂ emissions per unit change in demand at a given time and energy form.
• Leverage the Karush-Kuhn-Tucker (KKT) conditions of the LP to efficiently compute CO₂ intensity sensitivities without re-solving the optimization problem.
• Ensure consistency in CO₂ accounting by treating all energy forms equally in 'as-is' analysis and by applying marginal allocation rules in 'what-if' analysis.
• Validate the methods on two simulated test systems to compare results under varying storage and sector coupling conditions.

Experimental results

Research questions

• RQ1 How can time-dependent CO₂ intensities be accurately computed in multi-modal energy systems with significant storage and sector coupling?
• RQ2 What are the differences in CO₂ intensity values and implications between the 'as-is' and 'what-if' analysis approaches in dynamic energy systems?
• RQ3 How do large-scale energy storage and sector coupling affect the temporal variability of CO₂ intensities in renewable-rich energy systems?
• RQ4 Can CO₂ intensity sensitivities be computed efficiently using linear programming duality, and what are the computational advantages of this approach?
• RQ5 Which method—'as-is' or 'what-if'—is more suitable for informing local energy decisions, regulatory pricing, or CO₂ taxation policies?

Key findings

• Annual average CO₂ intensities fail to capture the true temporal variability of emissions in systems with high renewable shares and storage.
• The 'as-is' analysis yields time-varying CO₂ intensities that reflect actual emissions from all system components, including storage and conversion processes, and can produce counterintuitive results such as low intensities during high solar generation.
• The 'what-if' analysis produces time-constant CO₂ intensities for electricity in certain scenarios (e.g., CHP operation), as it reflects marginal emission changes due to demand shifts rather than actual emissions.
• The 'what-if' approach is more suitable for evaluating the impact of behavioral changes or investments, as it reflects the true marginal emission consequences of demand shifts.
• The 'as-is' method produces smoother, more intuitive results in some cases (e.g., high solar output), but can be less intuitive in complex configurations with circular dependencies.
• The proposed LP-based sensitivity computation enables efficient, real-time calculation of CO₂ intensity sensitivities, making the 'what-if' method practical for large-scale system modeling and policy applications.