## 5 Discussions  
This paper thoroughly addresses the issue of disturbance transient control in a lithium battery-supercapacitor hybrid energy storage microgrid, both theoretically and practically. Firstly, we constructed a hybrid energy storage system comprising a battery, supercapacitor, bidirectional _DC/DC_ converter, bus voltage, load-side disturbances and uncertain disturbances. Secondly, we trained the dynamic parameters \(k_{p}\) and \(k_{d}\) of the Active Disturbance Rejection Controller using a BP neural network. Utilizing the state observer within the ADRC, we quantified the uncertainties in the hybrid energy storage system based on system-identification methods. Finally, we conducted two significant simulation experiments to validate that the proposed method can effectively suppress load-side and uncertain disturbances within the hybrid energy storage system. The detailed conclusions of the simulation are as follows. We obtained the parameter values in Table 2 for the load disturbance-rejection curves. The LPV robust controller showed improvements over the PID controller in all metrics. Specifically, the \(IAE\) on the tracking voltage curves under various bus voltage inputs was reduced by approximately 3% and the \(rip\) values of the two controllers were reduced by 4.5% to 19%. The traditional Active Disturbance Rejection Controller (ADRC) further improved upon the LPV robust controller, with the \(IAE\) reduced by 3.9% to 6.35% and the \(rip\) values reduced by 0.56% to 6.68% under various tracking voltages. The BP neural network-based ADRC showed further reductions compared to the traditional ADRC. The \(IAE\) was reduced by 0.89% to 5.4% and the \(rip\) values were reduced by 1.7% to 5.98%. The tracking accuracy of the four controllers was nearly identical, with a negligible difference in \(rip\). Overall, the BP-ADRC controller demonstrated excellent load disturbance-rejection performance. Therefore, the proposed BP-ADRC controller can effectively suppress disturbances at the load end in a lithium battery-supercapacitor hybrid energy storage system. For the anti-uncertainty disturbance-simulation experiment, the following conclusions can be drawn from Figures 15-18: Firstly, the green simulation curve of the PID under various input bus voltages did not achieve real-time tracking of the bus voltage, with a deviation range of approximately 20-50 V. This indicates that the PID controller has lost its ability to track the bus voltage in the face of uncertainties, and the output voltage curve cannot meet the requirements of the hybrid energy storage microgrid, demonstrating its poor response to uncertainties. Secondly, the brown bus voltage-tracking curve of the LPV robust controller, although having smaller errors than the PID, also failed to achieve real-time tracking, with an error range of 0.5-3 V. This indicates that its bus voltage-tracking performance is affected by uncertainties, showing its inability to suppress disturbances caused by uncertainties effectively. Thirdly, although capable of tracking, the blue simulation curve of the ADRC exhibited significant oscillations with a real-time amplitude of 0.15-0.23 V. In contrast, the red bus voltage-tracking curve under the BP-ADRC controller achieved nearly perfect tracking, remaining smooth and oscillation-free throughout, demonstrating its excellent ability to suppress uncertainty disturbances. This is attributed to its ability to quantify uncertainty disturbances through a state observer and optimize parameters via a BP neural network. All the above data show that the BP-ADRC controller based on uncertainty quantization proposed in this paper is better than the PID controller, LPV robust controller and second-order linear ADRC controller for load disturbance and uncertain disturbance in a lithium battery-ultracapacitor microgrid.