Zero Current Switching Switched-Capacitors Balancing Circuit for Energy Storage Cell Equalization and Its Associated Hybrid Circuit with Classical Buck-Boost

: To overcome the problem of switching loss during the balancing process, a novel cell balancing circuit is proposed with the integration of a zero current switching technique. Moreover, the balancing circuit proposed can change between a classical buck-boost pattern and a resonant switched-capacitor pattern with ﬂexible control to cater to the balancing requirements under di ﬀ erent driving scenarios. The results of the simulation of ﬁeld experiments demonstrate successful balancing, various balancing speed, and low energy loss. The proposed balancing circuit proves to be e ﬀ ective for a wide range of application and is the ﬁrst attempt to integrate a dual balancing function in a single balancing circuit for cells.


Introduction
The pursuit of better battery performance has become the top challenge for electric vehicle (EV) design, as it primarily determines the driving mileage and manufacturing cost [1][2][3][4]. With the fast development of a supercapacitor (SC), the battery and SC strings composed of a large number of series and parallel-connected cells are usually used to formulate a hybrid energy package for better power performance [5][6][7][8]. Moreover, increasing numbers of researchers are collecting retired batteries for second-life application, hoping to cut costs while maintaining a qualified driving performance. Due to non-uniform individual cell properties, a certain imbalance may be easily generated among voltages of different cells during charging and discharging processes. As the effect of imbalance is accumulative and leads to battery deterioration, voltage balancing is necessary to guarantee the safe operation of the hybrid energy package [9][10][11].
Researchers have done many state-of-the-art works on promoting the balancing efficiency and balancing speed and decreasing loss. The passive balancing method is the most commonly adopted technique. Resistors in parallel with the cell strings are switched on when the cells get close to the peak withstanding voltage or when they have a higher state-of-charge (SoC) than other cells. This method generates additional heating loss because the energy dissipates into resistors during balancing process [12]. For energy-saving purposes, an active balancing method is put forward so that the charging and discharging current of each cell can be controlled to keep the same SoC among all cell units for the higher energy to be transferred into the cells with lower energy using a power converter circuit, instead of wasting it as heat loss. This method has proven to be more efficient, hence, many advanced voltage equalizers have been designed based on the active method using converters [13,14], switched-capacitors [15][16][17][18], transformers [7] or switched inductors [19,20].

Circuit Configuration
In this section, a series multi-functional balancing circuit is presented for analysis. Different states of EVs, such as the drive state, brake state, and park state, may have different requirements on the output power, balancing speed, and balancing loss. Figure 1 demonstrates six different operating modes with different cell balancing requirements for the corresponding driving states. For example, EVs in acceleration desire a high balancing speed and low loss while the park state does not have requirements on the balancing speed. The circuitry of Figure 2 shows the SC cells (SC 1 , SC 2 , . . . , SC n ) in series connection. In the n-cells voltage balancing system, there are n − 1 switched-capacitors and 4n − 4 switches which are dominated by the main intelligent control box to operate the circuit in different modes. All the switches are named in two groups S a and S b , the switches in each group are divided as S a2m−1 , S a2m , S a2m+1 and S a2m+2 , where m varies from 1 to n − 1; In S b2m−1 , S b2m , S b2m+1 and S b2m+2 , m varies from 1 to n − 1. This multi-functional balancing circuit has two operation states, buck-boost balancing and switched-capacitor balancing, under different control of inductors (L 1 , L 2 , . . . , L n−1 ) and switched-capacitors (C 1 , C 2 , . . . , C n−1 ). And the charge is transferred from a higher voltage SC to lower ones automatically. The proposed circuit changes its topology and parameters to cater to the operation requirements of different operation modes, such as the common drive mode, drive with air-conditioning mode, acceleration mode, brake mode, and park mode for EVs.

Balancing Circuit Operation Analysis
In an ideal case, the switching frequency f s should be equal to the resonant frequency f r .
where θ = R 2L ; R is the equivalent resistance, L is the inductance of the inductor and C is the capacitance of the switched-capacitor.
However, it is arduous to precisely match the RLC parameters of different balancing branches in real implementation. To avoid a reverse current of the resonant inductor, the switching frequency in the proposed switched-capacitor circuit should be slightly higher than the resonant frequency with regards to the tolerances of the RLC parameters.
There are two clock phase ϕ a and ϕ b in one switching period T, as shown in Figure 3. During the ϕ a , the switches S a2m−1 , S b2m−1 and S a2m+1 , S b2m+1 are turned on, the circuit forms the switched-capacitors resonant tanks series connecting with switched-capacitors as shown in Figure 4a,b. Meanwhile, Figure 4c,d are in a buck-boost mode state during the ϕ b , when S a2m−1 , S b2m−1 and S a2m , S b2m are turned on, there is only an inductor connect with SC. These two functioning modes operate alternatively with a high frequency control signal. They are divided into ZCS mode state I, ZCS mode state II, buck-boost mode state I and buck-boost mode state II which will be discussed in Section 2.3.

Analysis of ZCS Operation
When the switches S a2m−1 , S b2m−1 and S a2m+1 , and S b2m+1 are turned on, the circuit forms the switched-capacitors resonant tanks as shown in Figure 5. In the state of the ZCS-SC, charge will transfer from SC k to C k switched-capacitor tank when the voltage of SC k is higher than the initial voltage of C k . Therefore, C k is charged and the control signal during the process is shown in the top curve of Figure 5 and Table 1. In a similar way, the charge will transfer from C j to SC j when the voltage of SC j is lower than the initial voltage of C j . C j is discharged in this process and the control signal is shown in the bottom curve of Figure 5 and Table 1. SC k , C k , L k and SC j , C j , L j form the resonant loops. The r SC , r C , r S , and r L internal resistors for SCs, switched-capacitors, ON-resistance of the switches, and inductors, respectively. In order to simplify the operation analysis, the internal resistance will first be ignored. All the components are ideal.  (1) State I (See Figure 5 charging circle) In the state when S a2m−1 and S a2m+1 are turned on and S a2m and S a2m+2 are turned off. Assume that all the components here are ideal and there is zero internal resistance for the SCs, switched-capacitors, inductors, and switches in this analysis. The relationship between the current and the voltage are as shown below: where L k is the inductance of inductor L k ; V SCk is the voltage of SC k . Then, the variations of the V Ck and i r of the above are where ∆V Ck is the peak-to-peak amplitude of V Ck ; I r is the amplitude of the i r ; ω is the resonant angular frequency which is ω = 1 √ In this resonant period, assume that the initial voltage V Cmin across the capacitor C k is minimum voltage, which is lower than the voltage V SCk across the SC k . The initial voltage V Lk and the amplitude of the i r are: After half a resonant period, the voltage of the V Ck could reach maximum V Ck_max , which is shown below: (2) State II (See Figure 5 discharging circle) In the state when S b2m−1 and S b2m+1 are turned on and S b2m and S b2m+2 are turned off, the switched-capacitor C j is discharging SC j and the resonant current i r is increasing in the opposite direction. Similarly as state I, the amplitude of the resonant current is The voltage of V Cj could reach minimum V Cj_min at the end of this resonant period.
In fact, there are equivalent series resistance (ESR) for the components and the voltage drop across the switches that cannot be ignored. The r SC , r C , r S , and r L internal resistors for SCs, switched-capacitors, ON-resistance of the switches and inductors respectively should be considered in the following analysis. The total ESR R ESR in one resonant tank of the circuit is R ESR = r SC + r C + r L + 2r S .
The resonant current of charging and discharging state should be revised as: State I: State II: L k,j refers to either L k or L j in each of their state I and II and hence ρ and ω r are calculated according to their respective L k or L j in State I and State II. The maximum and minimum voltage of V Ck,j are

Modeling for ZCS Balancing Mode
As it is shown in Figure 6, SC cells can be formulated to be charged or discharged between each other with the equivalent resistance. In the resonant circuit, C k , L k and C j , L j has the same value C and L, respectively, and all the switches are the same. The voltage of V C could achieve the maximum V C_max at the end of the state I and be reduced to the minimum at the end of state II. The voltage ripple ∆V C can be obtained by subtracting (14) from (13).
In one switching cycle the quantity of electric charge is C∆V C , flowing from higher voltage cell to lower voltage cell. The average current I avg_r of one cycle is When ∆V C in (15) is substituted into (16), the equivalent resistance R eq of each resonant tank is The power loss P loss_r of the ZCS mode is shown below

Modeling for Buck-Boost Balancing Mode
During the progress of the buck-boost balancing mode, the charging/discharging varies in one cycle, the charge is transferred between SC k and SC j . The equivalent model of the balancing circuit is shown in Figure 7, where the ESR and the on-state voltage for the diode are included to facilitate modeling. To illustrate the voltage conversion process for the inductor L 1 , the mmf values of M _ch and M _disch to investigate the voltage conversion of the converter circuit for charging and discharging, respectively, during one cycle are where D 1 and D 2 are the turn-on duty ratio of switches for charging and discharging, respectively, D 1 + D 2 = 1.
Considering volt-second balancing of L 1 , the relationship between two cells is where R 1 = 2r S + r L + r SCk , R 2 = 2r S + r L + r SCj ; i ch and i disch are instantaneous current across L 1 for charging and discharging, respectively. I avg_ch and I avg_disch are the average current across L 1 when it is charging or discharging.
When t 2 t 1 i ch dt ≈ I avg_ch DT and t 3 t 2 i disch dt ≈ I avg_disch (1 − D)T, I avg_ch could be obtained from (21) as: The average current I avg_b of SC in this mode is In the balancing progress, all the energy transfers between each cell, from the higher voltage SC cell to lower voltage cell. During these states, the variation of the i ch is i ch (t) = I avg_ch + ∆i ch t − DT 2 (24) where ∆i ch is the current difference during charging state, T = 1 f s . The variation of the i disch is where ∆i disch is the current difference during discharging state. The energy discharged E disch from SC k and the energy charged E ch to the SC j throughout one cycle are: The energy transferred in the inductor L 1 is The energy loss E loss could be obtained by subtracting Equation (27) from (26).
where ∆i ch ≈ DV SCk 2L 1 f s . The power loss P loss_b of the buck-boost mode is

Simulation Results of the Multi-Function Voltage Equalizer
In PSIM software, the proposed circuit is simulated. The circuit topologies of three series connected SCs with initial voltages of 2.0, 2.4, 2.6 V, respectively, and with the same capacitance 1F are built in the simulation shown in Figure 8. Switched-capacitors C = 22 µF are used in simulation while f s = 15, 20, 25 kHz and 90, 100, 110 kHz of the control signals are used to operate the circuit. The above configurations are the same with practical application, except the capacitance of the SCs. Table 2 illustrates the comparison of the waveforms in the simulation varied with a different switching frequency f s for ZCS and buck-boost mode. It is observed that V SC1 , V SC2 , and V SC3 finally converge to the same voltage level in all circumstances. For the ZCS mode, when f s is larger, the switching speed is faster that accelerates the equalization process. Figure 9 shows the simulation results of the ZCS mode under 20 kHz frequency with 350 F SCs. At 32 s the balancing progress was about 10%, the voltage between V SC1 and V SC2 are 0.18 V at this moment. The balancing progress reached approximately 90% at 290 s when the difference reduces to 0.02 V. And the variations of the voltage of the switched-capacitor C 1 and current I 1 are shown in this figure.    Table 2 illustrates the comparison of the waveforms in the simulation varied with a different switching frequency fs for ZCS and buck-boost mode. It is observed that VSC1, VSC2, and VSC3 finally converge to the same voltage level in all circumstances. For the ZCS mode, when fs is larger, the switching speed is faster that accelerates the equalization process.   Table 2 illustrates the comparison of the waveforms in the simulation varied with a different switching frequency fs for ZCS and buck-boost mode. It is observed that VSC1, VSC2, and VSC3 finally converge to the same voltage level in all circumstances. For the ZCS mode, when fs is larger, the switching speed is faster that accelerates the equalization process.   Table 2 illustrates the comparison of the waveforms in the simulation varied with a different switching frequency fs for ZCS and buck-boost mode. It is observed that VSC1, VSC2, and VSC3 finally converge to the same voltage level in all circumstances. For the ZCS mode, when fs is larger, the switching speed is faster that accelerates the equalization process.  The balancing phenomenon conforms to the principles in Equation (16). When the switching frequency f s is the same as the resonant frequency f r the balancing progress could reach zero current when switches are turn on and off, this conforms to the principle in Equation (1). But the variation of the f s could not affect the balancing speed for buck-boost mode which is illustrated in Equation (23).

Experimental Results of the Multi-Function Circuit
The proposed circuit has advantages in performing balancing for different EV driving modes so that it is more flexible for an energy storage system which has different working conditions. To verify the mathematical derivation and software simulation, energy storage strings composed of three SCs were formulated with the multi-functional balancing circuit controlled by different switching signals. The topology is shown in Figure 8 and the list of components is recorded in Table 3. Figure 10 is the supercapacitor test platform used in the laboratory.
The voltage balancing process for the ZCS mode of the experiment is shown in Figure 11. The initial voltages of the SCs are 2.6 V, 2.31 V, and 1.88 V, respectively. After the voltage balancing was conducted, V SC1 V SC2 and V SC3 were all finally balanced to the same voltage magnitude, which coincides with the results in the above theoretical analysis. The integrated voltage magnitude after balancing was 2.23 V. Figure 12 depicts the voltage and current variations of C 1 , C 2 , and L 1 . It is clearly shown that when the switch turns on/off, the instantaneous current of the resonant loop is close to zero, which conforms to the principles of ZCS and loss reduction.
The voltage balancing process for the buck-boost mode of the experiment is shown in Figure 13. The initial voltages of the SCs were set as 2.42 V, 2.29 V and 2.03 V, respectively. After conducting voltage balancing, V SC1 V SC2 and V SC3 were also balanced to the same voltage magnitude, as expected. The integrated voltage magnitude after balancing operation was 2.17 V. Figure 14 depicts the voltage and current variations of L 1 . The energy loss of ZCS mode decreased 35% compared with that in buck-boost mode.      The experimental results demonstrate that the variations of both voltage and current in the proposed circuit conform to the charging/discharging principles analyzed in each phase.

Conclusions
A novel zero-current switching cell balancing circuit is proposed in this paper to decrease switching loss during balancing process. Furthermore, in order to adjust to different requirements of EV operation states, the multi-functional circuit was able to easily change between buck-boost and switched-capacitor pattern with flexible switching frequency and duty ratios. Simulation and field experiment were conducted to demonstrate its loss reduction effect and flexibility in various situations. The energy loss of the ZCS mode decreased 35% compared with that in the buck-boost mode. Future works may include voltage feedback control during the balancing process to further increase speed and decrease loss.