Braess’s paradox and power grid upgrades
http://phys.org/news/2012-10-power-grid-blackouts-braess-paradox.html
We went over Braess’s paradox briefly in lecture a while ago. When it appeared on the most recent homework and after reading the article “Power grid upgrades may cause blackouts, warns Braess’s paradox”, I was intrigued by the concept. Braess’s paradox is derived from modeling traffic networks. The paradox shows that adding more options to a network can sometimes actually harm it. In the case of traffic, adding roads can sometimes actually slow it down. This article relates Braess’s paradox to a power network; the study is the first time Braess’s paradox has been found in oscillator networks.
Due to the hurricane, there is an obvious increase in the demand of energy and power companies can add power lines. However, research found that adding certain new lines might cause power outages. On average, additional links are fine and stable but certain ones can decrease or destroy synchronization in the entire grid. The article discusses how this is a bit different than a traffic network, where braess’s paradox happens because of suboptimal Nash equilibrium, In Nash, drivers have no incentive to change their routes. However, if the system is not in Nash, driver’s can change to improve his or her own speed but will slow down the overall performance.
Here, with the power grid, the Braess’s paradox comes from “geometric frustration”. According to the article, “Adding a new link creates new cycles, along which all phase differences must add up to multiples of 2π to make all the phases well-defined. When a new link doesn’t satisfy this condition, it doesn’t synchronize with the other oscillators and the grid loses its phase-locked steady state.” The study also found that geometric frustration is more likely to occur in new power lines where many of the existing power lines are already heavily loaded which are morel likely to desynchronize. Based off of this, I wonder if that the same situation occurs to traffics where the more congested the traffic, the less suboptimal the Nash equilibrium is and there is more of a “paradox” which the more you add, the less helpful the condition is.