Differentiated Energy Services: Multiple Arrival Times and Multiple Deadlines *

The supply/demand balance problem plays a pivotal role in the electricity grid, especially when an increasing proportion of power is generated from renewable resources. Enormous supply/demand models have been put forward in order to handle the balance problem in the smart grid, in the presence of high renewable penetration. This has brought an awareness that the flexibilities in the demand can be exploited to alleviate the burden on the supply. In view of this, we apply and study differentiated energy services, which distinguish demands in terms of their available flexibilities. As a starting point, we concentrate on two problems regarding adequacy. On the one hand, we find both numerical and analytical ways to check the adequacy of a supply. On the other hand, we characterize the adequacy gap in the case of an inadequate supply.