Chapter 2Theories and Approaches of Large-Scale Complex Systems Optimization

Power systems are typical large-scale complex systems. With the development of smart grids and renewable energy, there has been a continuous evolution along this direction. In this chapter, we will give an outline of theories and approaches of large-scale complex systems optimization. The large-scale complex systems have multi-dimensional, highly interacting, and frequently stochastic characteristics [29]. Though the concept of large-scale systems emerges repeatedly for understanding and application, there is no precise definition for largeness nor generally acceptable quantitative measures of scale. However, there is still a clear distinction between large-scale systems and “small-scale systems”.

The following essential differences between large-scale systems and small-scale systems are clarified in Ho and Mitter [30].

  1. Presence of more than one controller or decision-maker, resulting in decentralized computations.
  2. Correlated but different information available to the controllers and possibly at different times.
  3. Requirements of coordination between the operation of the different controllers, resulting in hierarchical structures.
  4. Availability of only aggregated and highly imprecise models.
  5. Systems that may operate as a “team” or in an essentially conflicting manner; thus, there may be a single-objective function, multi-objective functions, or conflicting objective functions.
  6. It may be more reasonable ...

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