Energy storage can smooth the fluctuations of wind power integrated into the grid. Due to the strong adaptability of the empirical mode decomposition (EMD) algorithm to non-stationary signals, it is widely used in wind power smoothing control strategies. However, traditional EMD algorithms cannot guarantee that the upper and lower areas of the calculated intrinsic mode functions (IMFs) are equal, which tends to result in imbalanced calculated energy storage power and thus exceeding the limit of energy storage capacity. Focusing on wind power smoothing control by energy storage, this paper proposes a strategy based on the area-equilibrium EMD, which modifies the upper and lower areas of the IMFs to achieve a more balanced distribution. As a result, the IMFs contain less energy, and consequently, the energy contained in the calculated smoothing power is also reduced. This makes the energy storage capacity less likely to exceed the limit, thereby achieving better wind power smoothing performance under given energy storage capacity. Case studies show that the proposed strategy results in more balanced upper and lower areas of the IMFs, reduces the fluctuating range of calculated energy storage, and improves the wind power smoothing effectiveness.