The purpose of the wind-solar complementary system (WSCS) is to couple wind power and photovoltaic (PV) in a complementary way to strengthen the ability to generate power continuously in the medium and long term. However, due to the uncertainty of natural resources, the power output of WSCS is still unstable. In recent years, hybrid energy storage systems (HESS) have been used to match the WSCS to reduce the volatility of system output, but there are still some problems leading to the system's economic cost making it difficult to control. For example, the coupling relationship between wind and solar is linear, and the premise of the fluctuation smoothing strategy is to meet the power demand of load-side or grid-connected. In order to solve the mentioned problems, this paper proposes a method that HESS smooths fluctuations of wind-solar coupling power considering multi-scenario planning. By constructing a nonlinear coupling relationship between wind and solar and optimizing the capacity allocation of power source-side hybrid energy storage, the system accommodation characteristics for power fluctuations are improved.

Firstly, the marginal distributions of the two power sources are constructed using KDE based on the historical data of wind power and PV, and the joint distribution is obtained by preferably using the Gumbel-Copula functions. The multi-scenario set obtained by random sampling of the joint distribution is able to reflect the intensity of the fluctuation changes. Secondly, the FFT and its IFFT are used to analyze the spectral analysis of the unstable power in scenarios set to determine the power borne by each energy storage unit. In this part, since the multi-scenario ensemble originates from a joint distribution, the correlation of each scenario in the ensemble is consistent, which means the cut-off frequency that distinguishes battery and super-capacitor does not change with the change of scenario. Finally, an optimization model is established with the objective function of minimum the cycle operating cost of HESS, and the capacity configuration of the HESS is calculated using an improved PSO. The result of capacity configuration provides room to accommodate fluctuations in power source-side output, which reduces the instability of the system.

The results of the simulation example show that the increase in frequency deviation before the HESS configuration is much larger than that after the HESS configuration. The change rate of RMSE for calculating the frequency deviation before and after the configuration of HESS ranges from 60.0% to 83.5%, the change rate gradually increases with the increase of the number of scenarios in the ensemble. This suggests that the role of HESS in regulating frequency increases as the number of scenarios increases. Meanwhile, with the increase in the number of scenarios in the set, the maximum growth in the rated power and rated capacity of the batteries is 77.1% and 54.9%, respectively. And that of the super-capacitors is 40.0% and 42.4%. However, this makes the increase in equipment cost of the super-capacitor more prominent. Further, the configuration of HESS makes the power fluctuation of the system at adjacent moments smoother. The fluctuation accommodation range of the power source-side within the time intervals of 10 h, 60 h, and 240 h is enhanced by 12.9%, 7.4%, and 6%, respectively. The amplification of the fluctuation accommodation range decreases with the longer of the time intervals. Nevertheless, the HESS still has rechargeable power characteristics when the power source-side output is zero.

From the simulation results, the following conclusions can be drawn: (1) Different numbers of scenarios in the set have consistent correlation, so the dividing frequency of the battery and the super-capacitor does not change with the number of scenarios, which makes the HESS can be effective for the fluctuating power to modulate frequency. (2) The more complex the frequency variations of the fluctuating power at the wind-solar coupling output, the more pronounced the capability of HESS modulating frequency. (3) The results of the HESS configuration reflect that super-capacitors and batteries have greater advantages in the rated power and rated capacity, respectively. (4) Even if the wind-solar coupling output is close to 0 or 0 after the configuration of HESS, the system is still able to ensure that there is a certain margin to counteract the fluctuating impact of sudden power changes.