  Energy storage (ES) can help decarbonize power systems by transferring green
renewable energy across time. How to unlock the potential of ES in cutting
carbon emissions by appropriate market incentives has become a crucial, albeit
challenging, problem. This paper fills the research gap by proposing a novel
electricity market with carbon emission allocation and then investigating the
real-time bidding strategy of ES in the proposed market. First, a carbon
emission allocation mechanism based on Aumann-Shapley prices is developed and
integrated into the electricity market clearing process to give combined
electricity and emission prices. A parametric linear programming-based
algorithm is proposed to calculate the carbon emission allocation more
accurately and efficiently. Second, the real-time bidding strategy of ES in the
proposed market is studied. To be specific, we derive the real-time optimal ES
operation strategy as a function of the combined electricity and emission price
using Lyapunov optimization. Based on this, the real-time bidding cost curve
and bounds of ES in the proposed market can be deduced. Numerical experiments
show the effectiveness and scalability of the proposed method. Its advantages
over the existing methods are also demonstrated by comparisons.
