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  1. An increasing share of consumers care about the carbon footprint of their electricity. This paper analyzes a method to integrate consumer carbon preferences in the electricity market-clearing by introducing consumer-based carbon costs and a carbon allocation mechanism. Specifically, consumers submit not only bids for power but also assign a cost to the carbon emissions incurred by their electricity use. The carbon allocation mechanism then assigns emissions from generation to consumers to minimize overall carbon costs. Our analysis starts from a previously proposed centralized market clearing formulation that maximizes social welfare under consideration of generation costs, consumer utility, and consumer carbon costs. We then derive an equivalent equilibrium formulation that incorporates a carbon allocation problem and gives rise to a set of carbonadjusted electricity prices for both consumers and generators. We prove that the carbon-adjusted prices are higher for lowemitting generators and consumers with high carbon costs. Further, we prove that this new paradigm satisfies the same desirable market properties as standard electricity markets based on locational marginal prices, namely revenue adequacy and individual rationality, and demonstrate that a carbon tax on generators is equivalent to imposing a uniform carbon cost on consumers. Using a simplified three-bus system and the RTSGMLC system, we illustrate that consumer-based carbon costs contribute to greener electricity market clearing both through generation redispatch and demand reductions. 
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    Free, publicly-accessible full text available January 1, 2027
  2. An increasing number of corporations and individuals are interested in minimizing the carbon footprint of their electricity use. In order to do this, they must have access to a ’carbon signal’ that quantifies the real time emissions intensity of their supply of electricity. One promising carbon signal is Locational Marginal Carbon Emissions (LMCE). However, as LMCE is often not available, Locational Marginal Price (LMP) is often suggested as an proxy for LMCE. This paper seeks to contribute to the evaluation of LMP as a potential signal for informing carbon-aware load-shifting. We evaluate the connection between LMCE and LMP via statistical analysis on real data from the PJM system operator. Additionally, we conduct data-center load-shifting case studies using each of the signals. Our results show that while LMP and LMCE have a positive relationship for many samples, there are also extremely highmagnitude exceptions to this pattern. Driven by such examples of ’misalignment’ between LMP and LMCE, our load-shifting case study shows the potential for large emissions increases when shifting based on LMP. 
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