If you're at least level 2 in Powerplay then you do have passive bonuses that apply when you undertake certain activities in a system controlled or exploited by your power. In our struggle to expand Azrael your Imperial Powerplay alignment can magnify the effects of specific activities.
In my case (at level 2 pledged to AD) any mission I take on behalf of any minor faction in a system controlled or exploited by the blue haired one increases the influence effects by 10%. For that reason alone I am seriously considering raising my pledge level to 3 in order to get the 15% influence boost. Aisling and Winters have the greatest influence effects on minor factions among all the Powers.
Note through that some bonuses appear to be bugged, Mahon's and Torval's in particular.
https://forums.frontier.co.uk/showthread.php?t=151144(From level 2-5)
Aisling Duval - Imperial Con Man - 10%/15%/20%/25% Influence change
Archone Delaine - Jabba the Hutt - 20%/30%/40%/50% Bounty reduction
Denton Patreus - Arms Dealer - 5%/10%/15%/20% Reduced weapon prices
Edmund Mahon - Alliance Salesman - 5%/10%/15%/20% Increased Trade profits
Felicia Winters - Federal Con Man - 10%/15%/20%/25% Influence change
Lavigny-Duval - Imperial Boba Fett - 20%/30%/40%/50% Increased bounty money
Li Yong-Rui - Insurance Salesman - 5%/10%/15%/20% Insurance reduction
Pranav Antal - Independant Con Man - 5%/10%/15%/20% Influence change
Zachary Hudson - Federal Boba Fett - 20%/30%/40%/50% Increased bounty money
Zemina Torval - Imperial Salesman - 5%/10%/15%/20% Increased Trade profits
