I'm running a simulation to assess what my minimum detectable effect size for a synthetic control study where the sample size is fixed and I'm noticing a strange relationship between power and effect size. Normally you would expect that power and effect size have a logistic relationship where power grows as effect size increases and then levels off (s-shaped curve). What I'm observing however is a u-shape, where power is high for low effect sizes, and again for high effect sizes, following this pattern. The MDE in the figure below is a relative effect size, so 1.001 is a 0.1% lift in the metric.
Is this a valid form for the relationship between effect size and power or is it possible this is happening due to random variation?
Thank you for the help!