Braess Paradox in Electrical Networks – When more might mean less
J. Rojas, A. Alonso and D. Quesada
School of Science, Technology and Engineering Management, St. Thomas University, Miami Gardens FL 33054
Electrical grids are part of the network of connections maintaining a city alive nowadays. Many times we see a limited amount of lines and poles, as well as, supportive local electrical transformer points (LETP). Most of these connections are wired in parallel in order to guarantee a sustainable flow of electricity plus being robust enough against failures. Why are we not making the system redundant and increasing the number of grid points and cabling? How the performance of a power grid network can be assessed from its connectivity pattern? In this presentation the Braess Paradox is investigated for several network configurations. Special interest is dedicated to the Wheatstone bridge and to those networks containing such configurations as part of their structural elements. The flow across the network as well as the overall resistance are computed and expressed in terms of network characteristics. In answering the first question, we hypothesized that despite of the economic cost of such approach there is a counter intuitive fact known as the Braess Paradox, which states that in a congested network, it may happen that adding a new path between destinations can increase the level of congestion. In transportation networks, the phenomenon results from the decisions of network participants who selfishly seek to optimize their own performance metrics. In an electric power distribution network, an analogous increase in congestion can arise as a consequence of Kirchhoff's laws. To address the second question, we also hypothesized that power grid performance might be assessed through a combination of indices characterizing networks and enabling quantify the easiness of connecting two distant points by walking the shortest path. The results obtained from executing these methods included: power grids can be mapped into networks of vertices (hubs) and edges (connecting lines); power grid networks can be studied through the Adjacency Matrix, Geodesic Paths, and Clustering coefficient; electrical networks behave similar to Road networks. In both cases, the addition of extra links (roads, connecting lines) yields to overloads and a detriment in performance. This fact is known as the Braess Paradox; for every network there is a critical value of edges above which, any addition does not introduce any improvement in performance; intelligent Dashboard can be implemented to control the performance of the power grid in parallel to the management windows.
