Effect size is one of the two major factors that contribute to power. Another factor is the number of scores in the sample.
Explanation:
As far as the power of a statistical tests are concerned, there are two major factors that directly affect it. These factors are namely the 'effect size' and 'number of scores'.
The bigger the effect size, greater is the power of the test. Also, the greater the number of score in the test sample, greater is its power.