Designing Carbon Policy with Profit-Maximising Energy Storage

We examine carbon-policy design for a power system with energy storage as well as renewable and fossil-fuelled generation. A central-planning solution internalises the environmental externality of carbon emissions and curbs fossil-fuelled generation in proportion to the marginal cost of damage. By contrast, a decentralised solution leads to a bi-level setup: an upper-level welfare-maximising policymaker sets a carbon tax to impose upon lower-level profit-maximising generators. For completely efficient storage, an optimal carbon tax in this bi-level setting renders the first-best outcome. However, with inefficient storage, an infinitesimal increase in the carbon tax induces prices to increase at the same rate. As a result, storage shifts energy to the off-peak period to offset the loss in the value of stored energy. Hence, relative to the marginal cost of damage from emissions under central planning, the optimal carbon tax for the decentralised case is lower and may be nonmonotonic in energy storage’s inefficiency.