Power Cords: A Skeptic Looking to Dabble...

'the outlet could be an option, but I'm certainly not planning to get a dedicated line for this project'. :). You're just dabbling for a little better sound, right? Maybe a better power cord, right? You really don't want to notice an improvement, do you? Because you're happy with your current setup, right? Understand that if you take this step and things get better with just a little dabble, it won't be "a" step, it will be the "first" step. 8^). Enjoy.

If I were in your position I would proceed as follows...

First step - replace the outlet
Second step - replace the source power cord
Third step - replace the power amp power cord

Pretty soon you'll be running :-)

Mceljo...
"seems that there should be some science to it"

Without getting too complicated - The science is related to a couple of
main factors...

FIRST- component power supply and it's ability to store enough energy to
handle transient demand

High-end components have a large power supply with lots of headroom to
handle transient demands.

Modestly priced components have power supplies with less headroom.

With these components, what happens when transient demand excceds a
power supplies capability is a fluctuation in internal voltages that result in
distortions in the audio signal.

Being stereo, the distortions in the left and right channels tend to be
different and that causes a lack of focus in the image. There can also be
phase variations that also contribute to a poor image

A good power cord will contribute to those transient demands being better
satisfied resulting in a better image, which in turn improves clarity and
image.

SECOND - The quality of the conductors and connectors used on the power
cord

High quality copper in the cable and the connectors will ensure the best
performance from the power cable, in that they will quickly respond to
transient demand to replenish energy in the power supply from the mains.

Some of the more exotic power cables use conductor geometries to further
enhance their conductivity abilities.

In very general terms the improvements that power cables can make in
modest systems will include a tighter control of bass frequencies and a
more precise placement of instruments in the sound stage

Improvements that power cables can make in high end components can be

much more subtle and generally result in improvements in clarity, texture
and depth of image.

To complicate matters the quality of interconnects and speaker cables play

a huge role in the performance of a system and may not allow the full
potential of a power cable upgrade to be fully appreciated.

Lastly you have to understand the resolution capability of each of your
components and how that factors into the equation and how they may
allow or prevent the full potential of ANY cable upgrade to be fully
appreciated.

Bottom line it's complicated - many people will arrange an "at
home" audition in their system - that's the most fool proof method of
assessment.

Trying to apply "some science" takes many audio engineers a
lifetime in their quest for the ultimate component, interconnect, cable

Be smart - Let your ears be the judge.

As I said at the start, this narrative is a very generalised comment-
"without getting too complicated"

The issues are many and the combinations endless - the budget, a
constraint - generally :-)

but I'm certainly not planning to get a dedicated line for this project.

Dedicated lines should be the first step for power upgrades. Think of it as the power cord to the system from the service panel. Typical house wiring will be 14 gauge wire with many connections as it routes from one inexpensive outlet to the next, then finally gets to the system. Even if you upgrade the outlet at the system, you still have the connections through all the other inexpensive outlets. A dedicated line eliminates this.

Also, does it really make sense that you will achieve full benefit using a 9 gauge heavy duty power cord on the amp, when 14 gauge is feeding your wall outlet. Maybe a 10 gauge dedicated line should be the first step.