Complex Theory in Small Systems: An Application to the Bolivian Power System

The occurrence of blackouts in recent years and their impact on society call into question the traditional planning and reliability analysis, which focuses on events of significant chances, without explicitly considering the development of catastrophic situations such as blackouts. The complexity theory provides concepts widely applied in other areas, such as economics and science, opening a new field of study in electrical systems. This would provide complementary tools to traditional analysis, helping explaining, quantifying and modeling events with very low probability and high impact for society, such as blackouts and cascading failures. These new concepts are applied to characterize the Bolivian power system, marking the first application to a Latin American system. Results are surprising because of its failure behavior is consistent with a “power law”, suggesting a complex system, characterized by self-organized criticality (SOC) with long-term memory, where small perturbations can propagate out producing blackouts. This suggests that this theory would be appropriate not only to describe giant systems such as those from China and the U.S., but also for smaller systems, such as the Bolivian and other Latin American ones. It was shown that blackouts provide significant risks that would require explicit modeling and risk management.