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 . 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 .
- Presence of more than one controller or decision-maker, resulting in decentralized computations.
- Correlated but different information available to the controllers and possibly at different times.
- Requirements of coordination between the operation of the different controllers, resulting in hierarchical structures.
- Availability of only aggregated and highly imprecise models.
- 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.
- It may be more reasonable ...