Solving Braess’ Paradox in Electrical Power Grids
https://physicsworld.com/a/beating-braess-paradox-to-prevent-instability-in-electrical-power-grids/
http://iopscience.iop.org/article/10.1088/1367-2630/aad490
Braess’ Paradox happens when adding an extension route to a network actually impedes the traffic flow and lowers the efficiency. It does not only apply to cars and roads, but in electrical power grids as well. As the grids trying to adapt to the wider range of coverage and new kinds of renewable energy, they need additional transmission lines to increase the capacity of existing system. However, adding transmission lines can cause frequency fluctuation such as frequency drops, instability and blackouts based on the Braess’ Paradox. Traditional primary controls can only stabilize frequency when it drops but cannot restore it back to the normal Hz. In addition, not all generators in the current system has this kind of fast primary controls.
With analytical investigation and mathematical models, researchers have found that adding secondary controls between every two nodes can solve the Braess’ Paradox. In the class example, all drivers will choose the path containing the new highway to get from A to B. The only way to avoid the paradox is for drivers to make an agreement. Electricity cannot make an agreement, so we have to “force” them into alternative transmission lines. Too much energy going through one path will exceed max transmission capacity, and too little causes a frequency drop and thus leading to blackouts. With secondary controls, the frequency can be guaranteed at a stabilized fixed point and drops can be restored back to the reference point. Referring back to the class example, the paradox can be solved by limiting traffic on certain roads and offering a detour.
However, the researcher’s proposal is also questionable. It requires a secondary control in every two nodes within a power network, along with the consumer side, which is a large investment and effort. It may apply better to new networks where this feature is integrated in design at the beginning.