  Decarbonizing electric grids is a crucial global endeavor in the pursuit of
carbon neutrality. Taking carbon emissions from generation into account when
pricing electricity usage is an essential way to achieve this goal. However,
such pricing is not trivial due to the requirements of an effective electricity
market, such as maintaining budget balance, providing incentives to motivate
participants to follow the dispatch schedule, and minimizing the impact on
affected parties compared to when they were in the traditional electricity
market. Although existing joint electricity-carbon pricing mechanisms have
shown promising performance in reducing emissions in power networks, they can
hardly meet all the requirements. This paper proposes a novel joint
electricity-carbon pricing mechanism based on primal-dual optimality
condition-enabled transformation. An algorithm for determining the critical
market parameter is developed. The proposed pricing mechanism is proven to
possess all the desired properties, including budget balance, individual
rationality, dispatch-following incentive compatibility, and truthful-bidding
incentive compatibility. These properties ensure the proposed mechanism can
incentivize market participants to achieve carbon-aware social optimum in a
self-organized and sustainable way. Numerical experiments show the advantages
of the proposed pricing mechanism compared to the existing marginal-based and
carbon emission flow-based pricing mechanisms.
