This paper deals with the state of charge (SoC) estimation of a lithium-ion battery pack (LiBP) connected by some cells in series and parallel. The voltage noise, noise and current bias of current through the LiBP are taken into account in the SoC estimation problem. In order to describe the cell dynamic more accurately, especially for practical applications with charge and discharge amplitude varying suddenly, in this paper we use the second dynamic order model of the cell to estimate the SoC of the LiBP. By applying the sigma point Kalman filter (SPKF), the average SoC of the pack and bias current of current measurement are estimated by first estimator; the second estimator estimates the SoC differences of the cell modules from average SoC of the pack. The SoC of the cell modules are the sum of average SoCs of the pack and the SoC differences. By only using two estimators, the calculation complexity for SoC estimation is more reduced; this is very useful for the LiBP, which has the number of cells connected in a large series. This method was applied for the pack of SAMSUNG ICR18650-22P connected by seven cell modules; the cell modules were connected by nine cells in parallel; the LiBP was charged and discharged with amplitude varying suddenly. The estimated SoC of seven cell modules is smaller than 2% for a temperature operating range typically −5 °C to 45 °C. The comparison of the accuracy of SoC estimation based on the first and the second order dynamic models is made; the result shows that the SoC estimation used the second order dynamic model is more exact.

The optimal state of charge (SoC) balancing control for series-connected lithium-ion battery cells is presented in this paper. A modified SoC balancing circuit for two adjacent cells, based on the principle of a bidirectional Cuk converter, is proposed. The optimal SoC balancing problem is established to minimize the SoC differences of cells and the energy loss subject to constraints of the normal SoC operating range, the balancing current, and current of cells. This optimization problem is solved using the sequential quadratic programming algorithm to determine the optimal duties of PWM signals applied to the SoC balancing circuits. An algorithm for the selection of the initial points for the optimal problem-solving process is proposed. It is applied in cases where the cost function has no decreasing part. Experimental tests are conducted for seven series-connected Samsung cells. The optimal SoC balancing control and SoC estimation algorithms are coded in MATLAB and embedded in LabVIEW to control the SoC balancing in real time. The test results show that the differences between the SoCs of cells converges to the desired range using the proposed optimal SoC balancing control strategy.

<abstract> <p>This paper proposes a design of energy balance circuit for two adjacent Lithium-ion battery cells in the cell string based on the modifying of the bidirectional CuK converter principle. This design only uses one MOSFET to transfer energy between two cells in a direction controlled by the first relay, second relay controls the cutting energy balance circuit off the cells when they have the same energy level. The control command sent by the management battery system (BMS) to the energy balance circuit via an RS485 communication protocol controls the direction of transferring energy, the amplitude of the balance current, the frequency and duty of PWM, the PWM signal applied to MOSFET is programmed by a microprocessor PIC18F2685. This design overcomes some disadvantages caused by applying the principle of bidirectional CuK converter to design the energy balancing circuit, these are the need for a multiple level DC source to open MOSFETs and issue of the energy loss on the elements of energy balance circuit. This design is also easy to expand for the battery string with a large number of cells. The energy balance control strategy can be implemented directly by each the energy balance circuit or remotely by BMS using RS485 communication. The experimental results of online optimal energy balance control based on state of charge (SoC) feedback for 07 SAMSUNG 22P battery cells connected in series are presented to prove the efficiency of the energy balance circuit design for two adjacent cells proposed in this paper.</p> </abstract>

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This paper proposes a method to estimate state of charge (SoC) for Lithium-ion battery pack (LIB) with 𝑁 series-connected cells. The cell’s model is represented by a second-order equivalent circuit model taking into account the measurement disturbances and the current sensor bias. By using two sigma point Kalman filters (SPKF), the SoC of cells in the pack is calculated by the sum of the pack’s average SoC estimated by the first SPKF and SoC differences estimated by the second SPKF. The advantage of this method is the SoC estimation algorithm performed only two times instead of 𝑁 times in each sampling time interval, so the computational burden is reduced. The test of the proposed SoC estimation algorithm for 7 samsung ICR18650 Lithium-ion battery cells connected in series is implemented in the continuous charge and discharge scenario in one hour time. The estimated SoCs of the cells in the pack are quite accurate, the 3-sigma criterion of estimated SoC error distributions is 0.5%.