I read this article concerning the detection of Braess Paradox on power transmission networks: http://phys.org/news/2012-10-power-grid-blackouts-braess-paradox.html
Here is a quote from the article:
In the power grid scenario, on the other hand, the paradox originates due to what the researchers call "geometric frustration." 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. Witthaut explained the underlying mechanism using an analogy of a motor and generator.
My question is, why must the cyclic sum of the phase differences add up to a multiple of $2 \pi$ for the phases to be well defined?