Modeling Time-dependent CO$_2$ Intensities in Multi-modal Energy Systems with Storage

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.