I was taught a Kiai system by one of my Aikido teachers which relates specific sounds to specific directions;
Ey! – straight forward e.g. punch
U! – inward e.g. pulling in whilst striking like at the beginning of Jon’s Heian Nidan – this would be a compound Kiai; UEy!
Ee! – downward e.g. when throwing or groin strikes.
Ah! – expanding outward e.g. knife hand/soto uke.
Oh! – upward e.g. rising block.
I have worked with theses for years and it is second nature now.
I don’t know if the matching of the sounds to the movement really makes a difference in terms of strength or wether it seems to now simply because of psychological association.
However, it might be interesting to experiment with different Kiai sounds and see if it seems to make a difference to the feel of your movement.