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Center for Nonlinear Studies |
While many large infrastructure networks, such as power, water, and natural gas systems, have similar properties governing flows, these systems have distinctly different sizes and topological structures. This paper seeks to understand how these different features can emerge from relatively simple design principles. Specifically, we seek to describe the conditions under which it is optimal to build decentralized network infrastructures, such as a microgrid, rather than centralized ones, such as a large high-voltage power system. To investigate this question, we consider a network design problem for a system planner who seeks to deliver randomly distributed resources to randomly distributed end-users in a way that minimizes the total capital and operational cost of providing services and minimizes the magnitude of services not delivered. This network design model is formulated as a mixed-integer program with a novel method of representing security type constraints like those normally found in power systems analysis. While our method is simple it is useful in explaining why sometimes, but not always, it is economical to build large, interconnected networks and in other cases it is preferable to use smaller, distributed systems. The results indicate that there is not a single set of infrastructure cost conditions that cause a transition from centralized networks being optimal, to decentralized architectures. Instead, as capital costs increase network sizes decrease gradually, according to a power-law. However, as the value of reliability increases network sizes increase abruptly---there is a threshold in the value of reliability at which large, highly interconnected networks are economically justified. And as the value of reliability increases the relationship between capital costs and network sizes becomes even more sudden. We also motivate our use of these types of design models with an example of electricity network design in a developing country, using mobile phone data to characterize spatial heterogeneity in demand for energy services.
Host: Beth Hornbein