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• An adaptive droop method based on a superimposed frequency is proposed to balance the SoC among distributed BEUs. • By using the introduced AC reactive power to adjust the reference voltage according to differences in line resistance. • Voltage restoration is performed to maintain the average output voltage of the BEU at the nominal value. The conventional droop method for load sharing control in DC microgrid suffers from poor power sharing and voltage regulation, which affects the State of Charge (SoC) balance of distributed Battery Energy Units (BEUs). In this paper, an adaptive droop method based on superimposed frequency is proposed to balance the SoC among distributed BEUs. Accurate current sharing is achieved by using the introduced AC reactive power to adjust the reference voltage according to differences in line resistance. With the proposed SoC balance control method, the SoC balance among BEUs can be guaranteed by the accurate current sharing regardless of the different line resistances in the DC microgrid. In addition, voltage restoration is performed to maintain the average output voltage of the BEU at the nominal value. The effectiveness of the proposed control system is verified by simulation and HIT experimental tests. [ABSTRACT FROM AUTHOR]

• Luenberger observer and MRAS algorithm to estimate the load characteristic parameter changes. • Cost Function with PI term of the speed error to eliminate steady-state speed error and improve the robustness of FCS-MPDSC parameters. • Finite control set model predictive direct speed control (FCS-MPDSC) to achieve fast speed response performance. Model predictive control (MPC) is an advanced control method that relies on a mathematical model containing the motor parameters in the field of Permanent Magnet Synchronous Motor (PMSM) application. However, the internal parameters of the motor and external load characteristic parameters are uncertain, and their actual values ​​may be inconsistent with the nominal values, resulting in prediction errors, which in turn affect the performance of the control algorithm. Based on the analysis of the parameter sensitivity of the motor prediction model, traditional finite control set model predictive direct speed controller (FCS-MPDSC) predicts state parameters based on a mathematical model, and there is a problem that the parameters of the motor model are uncertain, which will lead to prediction errors. In order to improve the robustness of FCS-MPDSC parameters, this paper proposes an improved FCS-MPDSC for PMSM application, which abandons the traditional PMSM control cascade structure and has the advantages of fast speed response performance, small speed error and strong parameter robustness. In order to solve the problem of load characteristic parameter uncertainty, Luenberger observer and the Model Reference Adaptive System (MRAS) algorithm are used to estimate the variation of load characteristic parameters in this paper. Moreover, a proportional-integral (PI) control term of speed error is introduced into the cost function to achieve the zero steady state error of speed and torque, which make full use of the robustness of integral action and also a faster dynamic response of direct speed control is maintained. In this paper, the HIL experimental platform is built according to the simulation. The proposed method reduces the steady-state error of the traditional method under the parameter mismatch. When the inductance parameter and the permanent magnet flux parameters deviate two times larger than nominal values, the steady-state error of the motor speed are 0.1125% and 0.8725%, respectively, demonstrating the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]