## Materials and Methods
### Charge and Discharge Control Strategy  
The discharging of a battery generally follows a simple constant-current discharge or a constant-voltage discharge process. In this study, the simpler constant-voltage control was employed. In order to maintain its stability, the bus voltage was selected as the feedback voltage to achieve constant-voltage discharge. In this study, we used voltage model SG3525 to complete the constant voltage discharge control of the push-pull boost. A three-stage charging method is more beneficial to fully protect the battery and to ensure charging efficiency. However, the fixed charging curve does not consider the effects of instability and high randomness in the photovoltaic input on the battery charging process. The supply of unstable power can result in an excessive charging voltage or an insufficient charging current, and can also lead to battery over-discharge when there is continuously no power supply to the battery because of long-term insufficient sunlight [6]. Therefore, this study employed an enhanced four-stage charging method, in which a maximum power point tracking (MPPT) [14; 15] was combined with the conventional stage charging method with the addition of a pre-charging stage [13; 16; 17; 18]. The conventional stage charging method can be divided into constant-current charging, constant-voltage charging, and floating charging stages. Considering the particularity of the photovoltaic system, the following conditions should be satisfied:  
1. First, determine whether the battery is over-discharged; if this is the case, the battery should be trickle pre-charged with a current of 0.05 C for activation. 2. After activation, the battery enters the constant-current charging stage. However, the maximum charging current that the battery can receive is limited; therefore, the charging current should be limited to the maximum charging current I\({}_{\text{max}}\) (0.2 C) when the photovoltaic output power is greater than the battery receiving power. At this moment, the photovoltaic system does not work in the MPPT state. When the photovoltaic output power is lower than the battery receiving power, the photovoltaic system is maintained in the MPPT state. Although the battery is still in the constant-current charging stage, the charging current is lower than the maximum charging current. 3. During the MPPT constant-current charging stage, the battery voltage gradually increases with respect to the charging time. When the battery voltage increases to the maximum charging voltage, U\({}_{\text{max}}\), the constant-current charging stage is terminated, and the battery enters the constant-voltage charging stage, in which the charging current slowly decreases. 4. When the current decreases to a certain value in the constant-voltage charging stage, that is, I\({}_{\text{off}}\), the battery charging voltage is reduced to perform trickle floating charging. Figure 1: Schematic of charging and discharging system of lithium titanate battery. ADC: analog-to-digital converter; PWM: pulse-width modulation. Figure 2 shows the charging curve described above. Figure 3 shows the flow chart of the charging algorithm. When the problems of busbar stability and photovoltaic MPPT are not considered, constant-voltage and constant-current charging using voltage and current single loops can meet the requirements. However, from safety and stability viewpoints, the stability of the bus voltage in a photovoltaic charging system should be considered [19; 20]. Therefore, a bus voltage loop should be included so as to maintain the stability of the bus voltage. During the MPPT charging process, the stability of the busbar cannot be achieved by the interleaved parallel boost circuit, because the output controlled by the MPPT is the output power of the photovoltaic battery. At this time, the interleaved parallel boost circuit needs to execute the MPPT algorithm.