Envelope Modeling of Renewable Resource Variability and Capacity

One of the greatest challenges to integrating renewable energy resources into power operations is the variability in electricity output from these resources. The electricity system works essentially as a supply chain with a nearly zero tolerance for delay and storage resources that remain very limited despite rapid growth. Yet, because no consistent methodology exists to quantify the capacity contribution and system impact of variable generating resources such as wind and solar, these resources have yet to be effectively evaluated, managed, or compensated. To enable analysis of both renewable and traditional energy sources within the system, we adapt an envelope-based modeling method that is inspired by Network Calculus (NetCal) for deterministic queuing systems from the field of telecommunications engineering. The variability of electricity supply and demand can be described by upper and lower envelopes and their corresponding Legendre conjugates, which not only quantify variability across different time scales, but also characterize the tradeoff between any assigned capacity value and its corresponding Quality-of-Service (QoS) measures of performance. In particular, the QoS measure leads to an intuitive interpretation through storage resources. Envelope modeling leads to the definition of two QoS-based capacity metrics -- Guaranteed Capacity and Best-Effort Capacity -- whose conceptual and numerical properties we analyze and compare against existing capacity metrics. For illustration, the proposed methods are applied to data from the California Independent System Operator (CAISO). We also explicitly quantify the capacity contribution (via the notion of Best-Effort Capacity) of wind during peak hours and its negative system impact at night. The same envelope characterization further demonstrates the capacity value of storage resources