This article proposes a nonlinear distributed cooperative control scheme that can regulate the power output to achieve efficient utilization of renewable energy in ac microgirds, which ensures mean-square autonomous proportional power sharing over a nonlinear microgird system via a sparse cyber network subject to noisy disturbance and limited bandwidth constraints. The cyber networks are exposed to noisy disturbances and limited bandwidth constraints that terribly reduce the stability and quality of the whole system. To eliminate the adverse effects of noisy disturbances and limited bandwidth constraints, we propose a robust distributed control strategy designed by using partial feedback linearization for the dynamical nonlinear model of a microgrid system. Moreover, a distributed event detection mechanism with noise-dependent threshold is adopted to update the control signals with the consideration of unnecessary data communication reduction. Through adopting stochastic stability theory and Lyapunov function, the stability and convergence analysis of the proposed dynamic distributed event-detection conditions considering noise interferences is derived. As a result, the suggested method decreases the sensitivity of the system to failures and increases its reliability. Finally, a modified IEEE 34-bus test system in MATLAB/Simulink is utilized to verify the effectiveness of the proposed controller design scheme.