Directed energy phased array (DEPA) systems have been proposed for applications such as beaming optical power for electrical use on remote sensors, rovers, spacecraft, and future moon bases, as well as for planetary defense against asteroids and photonic propulsion up to relativistic speeds. All such scenarios involve transmission through atmosphere and beam perturbations due to turbulence that must be quantified. Numerical beam propagation and feedback control simulations were performed using an algorithm optimized for efficient calculation of real-time beam dynamics in a Kolmogorov atmosphere. Results were used to quantify the effectiveness of the system design with different degrees of atmospheric turbulence and zenith angles, and it was found that a large aperture DEPA system placed at a high altitude site can produce a stable diffraction limited spot (Strehl>0.8) on space-based targets for Fried length r₀≥10cm (at 500 nm) and zenith angles up to 60 deg, depending on atmospheric conditions. We believe these results are promising for the next generation of power beaming and deep space exploration applications.