In MATPOWER’s power flow, there is currently no way to explicitly specify the distribution of slack among multiple generators at the slack bus. The current convention, possibly completely undocumented, is to assign all of the slack to the first generator.
It has been pointed out that this is a source of ambiguity in terms of reproducibility of results for those using other software. Issue #63 <https://github.com/MATPOWER/matpower/issues/63> proposes a change to handling of the slack in such cases that would allow the slack to be distributed explicitly if the APF column in the gen matrix is given, otherwise split proportional to the relative size of the generator (i.e. equally for identically sized generators). Going forward, this would allow for explicit expectations for the slack solution for such cases. However, the downside is that it would break code that depends on the current handling. Any thoughts on how problematic that would be? Ray