Envelope Modeling of Renewable Resource Variability and Capacity

Innovation and Economic Growth, Networks, the Internet, and Cloud Computing and Cloud Computing

Article Snapshot


Xiaoyue Jiang, Geoffrey Parker and Ekundayo Shittu


Computers & Operations Research, Vol. 66, pp. 272-283, 2016


The output of wind turbines and solar cells varies widely, making them hard to integrate into power grids. This paper develops a new method to assess contributions from these energy resources, emphasizing that evaluators should focus on matching supply with demand.

Policy Relevance

Evaluators should assess individual power sources, not categories of sources. Smart grids will enable better matches of supply and demand.

Main Points

  • The output of solar and wind power generators varies widely compared with fossil fuel generators; renewable energy is hard to integrate into the existing electrical power system.
    • The power industry’s rules for managing renewable energy are arbitrary and conflicting.
    • The power system has high quality-of-service (QoS) standards, limited storage resources, and nearly zero tolerance for delay.
  • Telecommunications engineers use an envelope-based modeling method known as Network Calculus (NetCal) to evaluate Internet communications traffic.
    • Inspired by NetCal, this paper creates a new method for assessing the value of contributions from renewable energy sources.
    • The model considers the worst-case scenario, compatible with high QoS standards in electricity.
  • This paper’s modelling method describes each type of energy source in terms of its quality and quantity, evaluating individual generators (both conventional and renewable) rather than energy sources as a class; the model is tested using real data from wind farms, a solar farm, and a geothermal plant in California.
  • There is a strong correlation between the daytime output of solar systems and peak system load; when assessing the capacity of an energy resource, it is important to identify matches between supply and demand, focusing on service rather than on resources or equipment.
  • QoS assessments have two dimensions, guaranteed capacity and “best-effort” capacity.
    • The guaranteed capacity is the minimum value of the supply flow from a resource.
    • The “best-effort” capacity assess how much a resource can reduce overall load on the system.
  • The QoS assessments for solar and wind show that they complement one another, with wind producing considerable power over a long time period, and solar reliably producing power at peak periods on sunny days.
  • Storage systems should also be assessed in evaluating electrical system capacity; as more electrical cars are used, storage capacity will increase.

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