This study extends prior work on power analysis in two-level meta-analysis and provides methods on power analysis for univariate three-level meta-analysis. In a three-level hierarchical structure effect sizes are nested within studies, which in turn are nested within research groups of investigators. Consequently, the three-level model takes into account the between-study (second level) and the between-research group (third level) variances. The study provides closed form equations to compute the prospective statistical power of the z-test of the combined weighted average effect size. Illustrative examples that demonstrate the applicability of the methods in prospective power analysis are provided. Moreover, a simulation study is also conducted to demonstrate how prospective statistical power is modified by changes of the values of the design parameters that impact power within the context of the three-level model. Results indicate the third-level variance is inversely related with statistical power in three-level meta-analysis.