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Analytical methods are formulated in this paper to predict allowable distributed generation resources on a radial distribution feeder before voltage harmonic limits (as specified in IEEE 519-1992) are exceeded. The final result is a determination of allowable penetration levels of distributed generation resources for a range of distribution feeders. Closed-form equations are derived for typical feeder designs and different load allocation patterns. These equations are validated with conventional harmonic analysis simulations which show that the closed-form equation predictions are slightly conservative. These methods will serve as efficient tools for power system planning and design without requiring exhaustive studies to determine the impact of distributed generation resources.