Non-Equal Voltage Cell Balancing for Battery and Super-Capacitor Source Package Management System Using Tapped Inductor Techniques

Abstract

The battery management system (BMS) is the key development for energy storage systems, and battery balancing is an important subsystem of the BMS. However, with rapid development of supercapacitors, future energy storage cells are not constrained by one type, while different types of cells may form a source package (SP). Furthermore, the introduction of second-life batteries from retired electric vehicles promotes the demand of effective balancing systems for SPs with hybrid cells, as well as the requirement that balancing should be extended to any preset ratio rather than 1:1. This paper proposes a novel tapped inductor balancing circuit that allows any ratio of voltage balancing for hybrid energy storage cells. The analysis of the circuit, simulation and experiment results are presented to demonstrate its effectiveness in handling hybrid source balancing.

1. Introduction

Energy storage based on electrical means is an important development because several green energy systems such as electric mobility, power distribution and renewable energy sources need a vast amount of energy storage to ensure stable operation. Battery and supercapacitor (SC) are two prominent types, because they are already widely used and have proved to be cost effective. Circuit technology has been developed to prevent cell imbalance. Cell balancing is important because it avoids the overcharge and undercharge of cells to ensure safety [1,2].

In recent years, the campaign to solve out the recycling of a large number of aged batteries from retired electric vehicles has received increasing attention. It is known that retired batteries from electric vehicles still have 70 to 80% of state of health (SoH), which remains very useful for energy storage in stationery applications where the energy density is not in high demand; for example, the energy storage for peak-and-trough compensation from power plant, interruptible power supply and renewable energy storage systems.

Usually, single cells of battery/SC are packed into a source package. The cell voltage among different cells should be kept equal all the time to ensure that each cell is under the same operational condition. As not all the cells are identical, the cell balancing is therefore introduced and researched [3,4,5,6]. One of the most common types is to use classical switched-mode power converter buck-boost that is illustrated in Figure 1a. An inductor is used to transfer the excess charge from one cell to another using the buck-boost power conversion. The concept has been extended to couple an inductor to assist the balancing [7]. Figure 1b,c are two popular cell balancings that have been reported extensively. Figure 1b is based on switched-capacitor [8,9]. The method is similar to [10] where all cells are switched to common energy storage to equalize the voltage. Figure 1c is transformer-based and uses windings to balance each cell. [11,12] use a bi-directional switch with two anti-series MOSFETs to connect each cell to its balancing winding. Recently, the wireless power transfer approach for balancing is reported in [13] that uses an air-gapped transformer to conduct the wireless power transition. Recent research mainly focuses on the equal voltage balancing, i.e., mainly balancing cells of same type with voltage ratio of 1:1.

Table 1. Example of cell voltage for Li-ion batteries.

	LiCoO2	LiMn2O4	LiNi ⅓Mn ⅓Co ⅓O2	LiFePO4	Li4Ti5O12
Name	Lithium Cobalt	Lithium Manganese	NMC	Lithium Iron Phosphate	LTO
Energy Density (Wh/kg)	180	100	180	140	100
Cell Voltage (V)	3.7	3.8	3.8	3.2	2.2

shows an example of different voltages of Li-ion cells [14,15]. Currently, the source package is mainly composed of standardized battery cells with the same chemical combination and initial voltage.

The use of second life battery is getting popular [16,17,18]. Extensive research has been reported. Different combinations of cells may be connected in a battery pack or module [19,20]. The cells usually have different states of health, cell voltage and capacity. Also, there could also be a combination of battery and other energy storage devices such as SCs with different voltage levels. Even SC cells may have different voltages as well. Furthermore, in some circumstances, balancing among different source packages should be achieved. Therefore, an alternative balancing circuit with any voltage conversion is needed for universal application.

In this paper, a novel balancing circuit is proposed using tapped inductor techniques. Different from buck-boost converter and switched-capacitor, tapped inductor has advantages in step-free adjustment and is suitable for balancing hybrid source packages composed of SCs, batteries and aged batteries. Other converters such as H-bridge or resonant converter have been considered for suitable circuit for cell balancing, but will complicate the overall circuitry with added advantage of soft-cell balancing [21,22]. The rest of this paper is arranged as follows: Section 2 describes the basic circuit of the tapped inductor. Section 3 presents the circuitry of the tapped inductor balancing circuit. The modeling of the circuit is obtained in Section 4. The simulation and experimental results will be presented in the Section 5 and Section 6, respectively.

2. Tapped Inductor Basic Circuit

2.1. Conventional Buck-Boost Balancing

The conventional switched mode power conversion, buck-boost for example, can be used by adjusting different duty ratios of $Q_1$ and $Q_2$ to provide balancing for $S{C}_1$ and $S{C}_2$ in Figure 1. This is expressed as follows:

$$\frac{V_{S{C}_1}}{V_{S{C}_2}}=\frac{D_2}{D_1}$$

(1)

where $V_{S{C}_1}$ and $V_{S{C}_2}$ are the voltage of $S{C}_1$ and $S{C}_2$, respectively. $D_1$ and $D_2$ is the duty ratio of $Q_1$ and $Q_2$ respectively. It is noted that

$$D_1+D_2=1$$

(2)

When the voltage ratios of $S{C}_1$ and $S{C}_2$ are different in more than 2, the efficiency of the voltage conversion between $S{C}_1$ and $S{C}_2$ is low [23,24]. By using transformer concept or the isolated power converter such as forward converter or flyback converter, the efficiency of voltage conversion can be much higher when its transformer’s turns ratio is much larger. The concept has been developed widely and realized by tapped inductor converter [25].

2.2. The Tapped Inductor Basic Theory

Figure 2 shows a generalized circuit for three basic topologies in switched-mode power converter (SPMC). The transistor is connected to the tapped inductor L with the number of turns being m and the diode is connected to the tapped inductor with the number of turns being n. Since the magnetomotive force (mmf) is conservative for the tapped inductor, therefore, the voltage conversion ratio between $V_{in}$ and $V_o$ can be derived as follows.

To illustrate the voltage conversion for tapped inductor, the mmf values of M_on and M_off during the period when Q is turned on are:

$$M_{on}=m\frac{V_{Lm}}{L_m}{D}_{1}T$$

(3)

$$M_{off}=n\frac{V_{Ln}}{L_n}{D}_{2}T$$

(4)

where L_m and L_n are the inductance of the inductors with m and n turns, respectively. V_Lm and V_Ln are the voltage across L_m and L_n, respectively. D₁ and D₂ are the turn-on duty ratio of transistor and diode respectively.

(3) and (4) can be reduced to

$$\frac{V_{Lm}}{V_{Ln}}=\frac{m}{n}\frac{D_2}{D_1}$$

(5)

and

$$\frac{V_{Lm}}{V_{Ln}}=\frac{m}{n}\frac{\left(1-D_1\right)}{D_1}$$

(6)

$$D_1+D_2=1$$

(7)

For the application to the three basic topologies, the voltage conversion ratio k is then:

Buck converter:

$$\frac{V_o}{V_{in}}=k+1$$

(8)

Boost converter:

$$\frac{V_o}{V_{in}}=\frac{k-1}{k}$$

(9)

Buck-boost converter:

$$\frac{V_o}{V_{in}}=-k$$

(10)

where

$$k=\frac{m}{n}\frac{D_2}{D_1}$$

(11)

3. The Tapped Inductor Balancing

3.1. Basic Cell Equalization

Figure 1a and Figure 2c can be combined into a tapped inductor balancing that makes use of the large voltage conversion for input and output. The diode is changed into a MOSFET and therefore a bi-directional power flow can be obtained that allows the energy balancing between two different source packages. Figure 3a shows the topology that is also a buck-boost version. m and n are the number of turns obtained from the tapped inductor when the transistors Q₁ and Q₂ are on respectively.

The circuit analysis is similar to the conventional analysis of an SMPC. The voltage balancing equation then becomes:

$$\frac{V_{P_1}}{V_{P_2}}=\frac{m}{n}\frac{(1-D_1)}{D_1}$$

(12)

where V_P1 is the voltage of SP₁ and V_P2 is the voltage of SP_2.

In particular cases, if D₁ = 0.5, it is reduced to a transformer turns ratio to voltage ratio relationship:

$$\frac{V_{P_1}}{V_{P_2}}=\frac{m}{n}$$

(13)

In this case, each transistor is turned on for half a cycle in a complementary manner. The efficiency of such tapped inductor power conversion is high and using coupled-inductor’s turns ratio, any voltage conversion can be obtained, that is, balancing of battery or SC hybrid source packages under any voltage ratios can be achieved.

3.2. Generalized Cell Equalization

The above circuit can be extended to a string of i packages as shown in Figure 4. The xth tapped inductor L_x, coupled with source package SP_x, has a tapping and the turns ratio is $m_x:n_x$ where x varies from 1 to i − 1. The operation process of the proposed balancing system is divided into on state and off state with different switch signals V_{g_Q} and V_{g_S} in one cycle T as demonstrated in Figure 5. The balancing is self-adaptive and automatically converges to equilibrium. The current between the source packages could be close to zero when the voltages of the source packages are equal after balancing progress and the loss is small. The detailed operation principles of the two states are shown in Section 4.

The equalization equation for SP_x is:

$$\frac{V_{S{P}_x}}{V_x}=\frac{m_x}{n_x}\frac{(1-D_x)}{D_x}$$

(14)

where $V_{S{P}_x}$ is the voltage of the SP_x. V_x is the total voltage from SP_i to SP_x. D_x is the duty ratio of Q_x and S_x.

When all the SP voltages are balanced, D = 0.5 is adopted to maintain the equalization of the cell voltage. Based on (14), the voltage ratio could be further edited as:

$$\begin{array}{l}{V}_{P1}:V_{P2}:•••:V_{Pi-2}:V_{Pi-1}:V_{Pi}\\ =\frac{m_1}{n_1}\left(\frac{m_{i-1}}{n_{i-1}}+1\right)\left(\frac{m_{i-2}}{n_{i-2}}+1\right)\cdot \cdot \cdot \left(\frac{m_2}{n_2}+1\right):\frac{m_2}{n_2}\left(\frac{m_{i-1}}{n_{i-1}}+1\right)\left(\frac{m_{i-2}}{n_{i-2}}+1\right)\cdot \cdot \cdot \left(\frac{m_3}{n_3}+1\right):•••:\frac{m_{i-2}}{n_{i-2}}\left(\frac{m_{i-1}}{n_{i-1}}+1\right):\frac{m_{i-1}}{n_{i-1}}:1\end{array}$$

(15)

4. Modeling of Tapped Inductor Voltage Equalizer

4.1. Operation Principle and Average Current Analysis

During the progress of charging/discharging in one cycle, the charge is transferred between SP₁ and SP₂. The transistor is turned on and off and the circuit parameters vary accordingly. The equivalent model of the balancing circuit is shown in Figure 6. The equivalent series resistance and on-state voltage for the diode are included to assist the modeling.

Based on the relationship of (3) and (4), the mmf between SP₁ and SP₂ are

$$\frac{m}{L_m}{\displaystyle \int V_{L_m}d}t=\frac{n}{L_n}{\displaystyle \int V_{L_n}d}t$$

(16)

where $\frac{L_m}{L_n}=\frac{m^2}{n^2}$.

According to KVL, (16) could be further expressed as

$$\frac{V_{P_1}m}{L_m}DT-\frac{R_{1}m}{L_m}{\displaystyle \int i_{on}dt=}\frac{V_{P_2}n}{L_n}\left(1-D\right)T-\frac{R_{2}n}{L_n}{\displaystyle \int i_{off}dt}$$

(17)

where $R_1=R_{on}+R_{Lm}+R_{P_1}$, $R_2=R_{on}+R_{Ln}+R_{P_2}$. $R_{on}$ is the on-resistance of the switch; $R_{Lm}$, $R_{Ln}$ are the equivalent series resistance (ESR) of the inductor in m and n turns respectively, such that $\frac{R_{Lm}}{R_{Ln}}=\frac{m}{n}$; $R_{P_1}$ and $R_{P_2}$ are the ESR of the source packages; $i_{on}$ and $i_{off}$ are instantaneous current across L when the switch is on and off.

$I_{avg\_on}$ and $I_{avg\_off}$ are the average current across L when the switch is on and off, respectively, so that $\frac{I_{avg\_on}}{I_{avg\_off}}=\frac{n}{m}$.

Assume when ${\displaystyle \int i_{on}dt\approx I_{avg\_on}DT}$ and ${\displaystyle \int i_{off}dt\approx I_{avg\_off}\left(1-D\right)T}$, $I_{avg\_on}$ could be obtained from (17) as:

$$I_{avg\_on}=\frac{-\frac{m}{n}{V}_{P_2}\left(1-D\right)+V_{P_1}D}{{\left(\frac{m}{n}\right)}^2{R}_2\left(1-D\right)+R_{1}D}$$

(18)

The average current I_avg of SP₁ is

$$I_{avg}=\frac{-\frac{m}{n}{V}_{P_2}\left(1-D\right)D+V_{P_1}{D}^2}{{\left(\frac{m}{n}\right)}^2{R}_2\left(1-D\right)+R_{1}D}$$

(19)

4.2. Energy Conversion Loss Analysis

During balancing progress, all the energy transfers between source packages, from the higher voltage source to lower voltage source. In the end of the progress, each of the SP voltage is under the ratio shown in (15).

The variation of $i_{on}$ is

$$i_{on}(t)=I_{avg\_on}+\Delta i_{on}\left(t-\frac{DT}{2}\right)$$

(20)

where $\Delta i_{on}$ is the current difference during the on state.

The energy discharged E_dch from SP₁ throughout one cycle is:

$$E_{dch}\approx V_{P1}{\displaystyle \int i_{on}dt}$$

(21)

The variation of $i_{off}$ is

$$i_{off}(t)=I_{avg\_off}+\Delta i_{off}\left(t-\frac{DT}{2}\right)$$

(22)

where $\Delta i_{off}$ is the current difference during the off state.

The energy charged E_ch to the SP₂ is

$$E_{ch}\approx V_{P2}{\displaystyle \int i_{off}dt}$$

(23)

The energy transferred in the tapped inductors is $E_{Lm}=E_{Ln}$. The variation of $E_{Lm}$ and $E_{Ln}$ are presented below

$$E_{Lm}\approx {\displaystyle {\int }_{t_1}^{t_2}\left(V_{P1}-i_{on}{R}_1\right)}{i}_{on}dt$$

(24)

$$E_{Ln}\approx {\displaystyle {\int }_{t_2}^{t_3}\left(V_{P2}-i_{off}{R}_2\right)}{i}_{off}dt$$

(25)

By equaling (24) to (25), the energy conversion loss is

$$\begin{array}{l}{E}_{loss}\approx V_{P1}{\displaystyle {\int }_{t_1}^{t_2}{i}_{on}dt}-V_{P2}{\displaystyle {\int }_{t_2}^{t_3}{i}_{off}dt}\\ \hspace{1em}\hspace{1em} =R_1{\displaystyle {\int }_0^{DT}{i}_{on}^2}dt+R_2{\displaystyle {\int }_0^{\left(1-D\right)T}{i}_{off}^2}dt\\ \hspace{1em}\hspace{1em} =T\left(I_{avg\_on}^2+\frac{3\Delta i_{on}^2}{4}\right)\left[R_{1}D+R_2{\left(\frac{m}{n}\right)}^2\left(1-D\right)\right]\end{array}$$

(26)

where $\Delta i_{on}\approx \frac{V_{P1}}{2L_{m}f}$, $\frac{\Delta i_{on}}{\Delta i_{off}}=\frac{n}{m}$.

As shown in (26), the initial voltage of SPs, voltage ratio, frequency, inductance, duty ratio and ESR will affect the energy conversion loss.

5. Simulation Study

The above balancing process has been simulated by PSIM software to study the performance of the circuit. Assume that the source packages are composed of the SCs with the same capacitance 350F. For the tapped inductor, L = 400 µH is simulated while f = 30 kHz and D = 0.5 of the control signals are used to operate the circuit. The voltage ratio of $V_{P1}:V_{P2}:V_{P3}$ are simulated by 1:2:3, 1:2:4, 1:3:9 while according to (15), the turn ratios are 1:5, 1:6, 1:12 for L₁ and 2:3, 1:2, 1:3 for L₂.

Table 2. Simulation results of the Tapped Inductor voltage equalizer.

Voltage Ratio	1:2:3	1:2:4	1:3:9
Voltage Balance Waveform
X: Time (s); Y: Voltage (V)
Average Current Waveform
X: Time (s); Y: Current (A)

indicates simulation results of the waveforms for voltage balance and the average current under the schematic in Figure 7 with different voltage ratios. Because of the preset voltage ratio and initial voltages, SP₁ is discharged and SP₂ and SP₃ are charged for voltage ratio of 1:2:3; the SP₁ and SP₂ are discharged and SP₃ is charged for voltage ratio of 1:2:4 and 1:3:9. The voltage of each source package varies under the voltage ratio in the equalization process, and it is apparent that the balancing phenomenon conforms to the principles in (15). The variation of average current and energy loss in the simulations are consistent with the principles in (19) and (26).

6. Experimental Results

To verify the validity of mathematical derivation and software simulation, a 1:2:3 voltage ratio tapped inductor balancing circuit is built in laboratory and all the SPs are tested in the same ambient temperature (20 °C). The inductors are made in the laboratory with 1:5 and 2:3 turns ratio. All the transistors are continuously pulsed as the method in Section 3. Although the control method could be used to trigger the unbalanced cells to accelerate the balancing speed, because the unbalancing speed is slow as compared with the speed of balancing of proposed balancing circuit, therefore the present control is to use continuous triggering to all transistors and it reduces the control complication and the system is therefore absolutely stable. The balancing current will be reduced to zero when the equalization is achieved. Topology of the equalizer is shown in Figure 7 and the list of components is recorded in

Table 3. Parameters in the experiment.

Units	Quantity
Supercapacitor (DRL357S0TQ60SC)	6
Capacitance of SCs	350 F
ESR of SCs	6 mΩ
MOSFET (IRFR3607PBF)	4
On-state resistance of MOSFETS	7.34 mΩ
Inductance of L1	390.4 µH
Turns ratio of L1	1:5
Inductance of L2	386.9 µH
Turns ratio of L2	2:3
Switching frequency	30 kHz

. SP₁, SP₂, SP₃ are formed by one SC, two SCs and three SCs connected in series and the list of components is recorded in Table 3. The size of the components in the control circuit of this balancing circuit is much smaller than the SPs because the balancing current is only a very small percentage of the main current of the SP. The circuit is suitable for practical use.

The source packages, SP₁, SP₂ and SP₃ are charged to the initial voltages of around 2.01 V, 4.22 V and 7.18 V, respectively. The balancing process is started by enabling the gating signals of the equalizer prototype. The voltage balancing process of the experiment is shown in Figure 8. After the voltage balancing progress, all $V_{SP1}$, $\frac{V_{SP2}}{2}$ and $\frac{V_{SP3}}{3}$ are balanced to the same voltage magnitude, which coincides with the results of theoretical analysis. Besides, the average current and energy loss are close to the principles in (16) and (23).

Figure 9 and Figure 10 depict the voltage and current variation of tapped inductor L₁ and tapped inductor L₂ during 30 kHz frequency. The ripple of currents I₁, I₂, I₃ and I₄ is small. The experiment results demonstrate that the variation of all voltage and current conforms to the charging/discharging principles in the balance progress.

Retired batteries from electric vehicles have different voltage characteristics. For convenience of experiment, this paper took SC combination as the energy sources. However, as the tapped inductor balancing circuit proposed in this paper can be applied with any preset voltage ratio, the integration of second life batteries will not weaken the effectiveness of this non-equal voltage balancing technique. In practical design with PCB implementation, it is possible to keep the size of the balancing system at much less than one-tenth of the size of the whole packages with the proposed circuit topology. In theory, the inductor size can be further reduced by increasing the switching frequency. Therefore, the proposed method is a practical cell balancing solution for managing hybrid source packages with difference voltage ratios.

7. Conclusions

A new concept of source package equalization has been reported using a tapped inductor method. The method is derived from conventional tapped inductor converter. The advantage of the method is that it can allow cell balancing of any ratio with high efficiency. The proposed concept can be extended to several hybrid cells connected. Simulation and experimental results have been presented to demonstrate the effectiveness of this circuit. The proposed scheme is especially useful when second-life battery and other new types of energy are universally applied to energy storage systems, peak power compensation and even uninterruptible power supply.