Virtual synchronous generators (VSGs) with inertia characteristics are generally adopted for the control of distributed generators (DGs) in order to mimic a synchronous generator. However, since the amount of virtual inertia in VSG control is usually constant and given by trial and error, the real power and frequency oscillations of a battery energy storage system (BESS) occurring under load variation result in the degradation of the control performance of the DG. Thus, in this study, a novel virtual inertia estimation methodology is proposed to estimate suitable values of virtual inertia for VSGs and to suppress the real power output and frequency oscillations of the DG under load variation. In addition, to improve the function of the proposed virtual inertia estimator and the transient responses of the real power output and frequency of the DG, an online-trained Petri probabilistic wavelet fuzzy neural network (PPWFNN) controller is proposed to replace the proportional integral (PI) controller. The network structure and the online learning algorithm using backpropagation (BP) of the proposed PPWFNN are represented in detail. Finally, on the basis of the experimental results, it can be concluded that superior performance in terms of real power output and frequency response under load variation can be achieved by using the proposed virtual inertia estimator and the intelligent PPWFNN controller.