What is the rationale behind using (100%*x)^2 + (20%*x)^2, rather than (100%*x + 120%*x)^2?
With the two sources at opposite ends of the bus, even with a 200% rule, the current at any cross-section of the busbar never exceeds the busbar rating. So the heating from current in the busbar is never more than the worst case of the busbar carrying its full rated current along its entire length, e.g. via a single source at one end and a single load at the other end.
The additional heating from a 120% rule or a 200% rule comes from the additional connections to the busbar, and the resistance of those connections (and if you like the heating from within the breakers at those connections). Take the simple model that every connection to the busbar has the same fixed resistance R (and if you like R can include the resistive heating of the breakers). Let's do the accounting only for the sources, since the worst case for sources and loads will be the same, so the overall worst case connection heating is just double the worst case source connection heating.
With a 120% rule the worst case for connection heating is one connection at 100% of the busbar rating, and one connection at 20% of the busbar rating. While the worst case for a 200% rule would be two connections, each at 100% of the busbar rating.
Hence the comparison I made, where x is the busbar rating, and we are looking at I
2R heating, omitting the factor of R.
Cheers, Wayne