Analysis, Design and Implementation of Flexible Interlaced Converter for Lithium Battery Active Balancing in Electric Vehicles

Abstract

With the widespread use of modern clean energy, lithium-ion batteries have become essential as a more reliable energy storage component in the energy Internet. However, due to the difference in monomers, some of the battery over-charge or over-discharge in battery packs restrict their use. Therefore, a novel multiphase interleaved converter for reducing the inconsistencies of the individual cells in a battery pack is proposed in this paper. Based on the multiphase converter branches connected to each lithium battery, this circuit realizes energy transferred from any cell(s) to any other cell(s) complementarily. This flexible interlaced converter is composed of an improved bi-directional Buck-Boost circuit that is presented with its own available control method. A simulation model based on the PNGV model of fundamental equalization is built with four cells in PSIM. Simulation and experimental results demonstrate that converter and its control achieve simple and fast equalization. Furthermore, a comparison of traditional methods and the HNFABC equalization is provided to show the performance of the converter and the control of lithium-based battery stacks.

I. INTRODUCTION

With the construction of China's smart grid, new energy vehicles have been being extensively used due to their environmental friendliness, loading controllability and close coordination with aggregators and charging stations [1]-[3]. As a source of power for new energy vehicles, battery cells are of vital importance in terms of power character [4]-[7]. Consequently, various equilibrium circuit topologies with control methods have been designed to decrease the hazards of battery pack inconsistencies [8]-[14].

In [8], a dual-input high step-up DC/DC converter with zero voltage turn-off (ZVT) is proposed to improve the efficiency of the converter using soft-switching techniques. Then with the increase of the power supply unit, the control complexity will be significantly increased, which will cause difficulties in engineering. In [9], a modular equilibrium system was proposed, which contain N cells and M equalizers. The deficiencies of this implementation lie in the complexity of its circuit structure and an unavoidable process to reach the primary balance by adjusting the states of twelve switching tubes. In [10], the topology of a time-sharing flyback converter is proposed, where any of the single cells in the battery stack can be equalized. Each cell shares one equalization module in the control gap of a low-power microcontroller. The transformer is applied to this topology, which limits the volume and weight of the converter to some extent. A novel switching circuit that requires none voltage estimation is proposed [11]. With a single-charge equalizer based on a multi-winding transformer, the energy transformed in a battery pack is delivered by the magnetic circuit of the multi-winding transformer, which inevitably leads to a huge quantity of magnetic loss. In [12], an innovative method of energy sharing control scheme was adopted to self-adapt the rate of charging for all of the cells, which fundamentally eliminates the difference in the state of charge (SOC) among batteries. Choosing a lossless DC power converter results in reaching equilibrium slowly. In [13], fast equalization was realized by a buck converter with an Adaptive Unscented Kalman (AUK) filter for SOC Estimation. When compared with traditional methods, its advantages include a simplified circuit structure, reduced energy loss and a fast response. The experiment only performed four cell balancing, which is difficult to expand and apply in large-scale series battery balancing. One approach to expanding the battery string scale is the use of natural equalization [14]-[16], where energy naturally flows to the cells and measuring sensor equipment is not required.

The standard solution to this problem is based on the flexible control method of battery cells in this paper. The proposed control method is derived from natural equilibrium, which eliminates the shortcoming of the current decrease in the later equilibrium stage. Natural control makes energy flow naturally between overcharged batteries and other batteries with forced energy donors and acceptors. In [17], the multiphase interleaved converter and its basic working principle have been discussed with only the simulation and experiment comparison under idle state. This paper supplements the experimental content of the charging and discharging process. In this paper, the unbalanced cells in a battery pack are mathematically described in an energy exchange matrix, as do the switching states, which converts the battery energy transfer path into a linear algebraic problem. To clarify the feasibility of the strategy proposed in this paper, the converter for battery balancing is built in PSIM. Finally, a number of experiments verify that the proposed control strategy transfers battery energy to other cells in the stack quickly and flexible. In addition, analysis and explanation of the loss and efficiency of the converter under different numbers of batteries.

This paper is organized as follows. Section II presents the working principle of the flexible multiphase interleaved converter and its mathematical formula derivation. Simulation and PNGV model are demonstrated in Section III. Furthermore, Section III also presents experiment and result analysis. Come conclusions and future work directions are provided in Section IV.

II. OPERATING PRINCIPLE AND DESIGN

A. Basic Design and Principle

A typical Buck-Boost circuit can only achieve unidirectional power transfer, while changing the original diode with a MOSFET transistor enables bidirectional energy exchange and a continuous current flow [18], [19]. The primary circuit of this equalization technology is shown in Fig. 1. The derived buck-boost converter makes power exchange from one overcharged cell to the others. Each equalizer is connected by an inductor between two cell subpacks. The two-cell equalization circuit is shown in Fig. 2. Each equalizer separates the cells into two sections, the upper section and the lower sections, whose energy can be mutually exchanged. This topology can also individually transfer the energy of any one cell to the other cells in a stack. When compared with a traditional equalization converter, it makes battery energy equalization more flexible and easier to expand. The expanded topology is shown in Fig. 3. Each equalizer in the multiphase interleaved converter divides the complete battery component into two adjacent continuous battery sub-packs. Furthermore, the equalization module that connected to the positive and negative terminals of the over-charged battery delivers the extra energy to all the other batteries in the pack.

Fig. 1. Bidirectional buck-boost converter.

Fig. 2. Unidirectional buck-boost circuit principle (QBH>QBL).

Fig. 3. Multilayer equalization circuit extended topology.

In the steady state, the integral of the applied inductor voltage must be zero.

\(\int_{0}^{T} u_{L} \mathrm{d} t=0\)       (1)

When S_H is in the on state, u_L=E. When S_H is in the off state, u_L=-u₀.

\(E t_{\mathrm{on}}=U_{0} t_{\mathrm{off}}\)       (2)

\(U_{0}=\frac{t_{\mathrm{on}}}{t_{\mathrm{off}}} E=\frac{t_{\mathrm{on}}}{T-t_{\mathrm{on}}} E=\frac{\alpha}{1-\alpha} E\)       (3)

B. Natural Spontaneous Balancing Control

The transistors of a converter work in a complementary driving mode, and their respective duty cycle is set by the formula of the input and the output voltage.

\(\alpha_{i}=U_{H i} /\left(U_{L i}+U_{H i}\right)\)       (4)

\(U_{H i}=\sum_{x=1}^{i} U_{c e l l x}\)       (5)

\(U_{L i}=\sum_{x=i+1}^{n} U_{c e l l x}\)       (6)

\(R_{i I N e q}=\sum_{x=1}^{i} R_{c e l l x}+R_{S H i}+R_{L i}\)       (7)

\(R_{i O U T e q}=\sum_{x=i+1}^{n} R_{c e l l x}+R_{S H i}+R_{L i}\)       (8)

\(\alpha_{i} U_{L i}-R_{i INeq} \alpha_{i} I_{L m}=\left(1-\alpha_{i}\right) U_{H i}+R_{iOUTeq}\left(1-\alpha_{i}\right) I_{L m}\)       (9)

\(I_{L m}=\frac{\alpha_{i} U_{L i}-\left(1-\alpha_{i}\right) U_{H i}}{\alpha_{i} R_{i I N e q}+\left(1-\alpha_{i}\right) R_{i O U T e q}}\)       (10)

The subscript i stands for the number of batteries in the input branch, i∈int [1; N-1], U_Hi is the input voltage of the cells, and U_Li stands for the output voltage of the cells. In constant duty cycle mode, the average voltage generated on one side of the inductor is equal to a portion of the voltage across the entire battery pack. If the voltage of the battery pack on both sides of the inductor is balanced, the potential at the other end of the inductor is also the same. That is to say, the two parts of the cells separated by the equalizer are offset by the effect of the inductance, and the balancing current is zero. If this is not the case, the current generated by the potential difference will flow through the inductor to balance the voltages of the two potentials. Table I shows the on-duty of each switch. In order to reduce the idle time of the equalizer, each switch operates in the complementary conduction mode.

TABLE I DUTY CYCLE RATE OF THE EQUALIZATION CIRCUIT

C. Forced Active Balancing Control

To reduce repetitive consumption caused by energy cycling loss in the balancing process, a forced active equalization control is designed and demonstrated. The current flow is in the direction illustrated by the arrow. This converter performs an intuitive equalization control of the front cell and the rear cell in Fig. 4. In mode I, turning the switch S_Li-1 on, the balancing current flows along the red arrow in Fig. 4(a). Then in mode II, turning off the switch S_Li-1, the balancing current flows along the red arrow in Fig. 4(a). Meanwhile, if the energy of an overcharged cell is delivered to the rest of the stacks, the above steps demands performed in a certain sequence, and the S_Hi needs to be turned on. In mode III, the balancing current flows along the blue arrow in Fig. 4(b). Then in mode IV, the switch S_Hi is turned off, and the balancing current flows along the red arrow in Fig. 4(b). Table II describes the status of the switches at each state. (0 for close; 1 for open).

Fig. 4. Equilibrium current path of any unbalanced battery. (a) Current path in mode I and mode II. (b) Current path in mode III and mode IV.

TABLE II SWITCHING STATE DURING EQUALIZATION

The equilibrium of the battery string containing N cells is mathematically proved. The working principle is described as follows. Provided that B_i is overcharged, the extra-energy should be delivered to the other batteries. The extra-energy, given off from Bi to Bn, is temporarily stored by the inductor L_i-1 where each of them contributes Δε₁ in state I. Then inductor delivers this part of energy to the batteries from B₁ to B_i-1 in state II. Then the energy, given off from B₁ to B_i, is temporarily stored by the inductor L_i where each of them contributes Δε₂ in state III. The inductor delivers this energy to the batteries from B_i+1 to B_n in state IV. The difference energy between the battery B_i and that of the whole battery stack is defined as Q_i. The amount of energy transferred from each one in the cells is described by equations (11) and (12).

\((n-i+1) \Delta \varepsilon_{1} /(i-1)-\Delta \varepsilon_{2}=Q_{i}^{extra} / n\)       (11)

\(-\Delta \varepsilon_{1}+i \Delta \varepsilon_{2} /(n-i)=Q_{i}^{extra} / n\)       (12)

The simultaneous equations are solved:

\(\Delta \varepsilon_{1}=(i-1) Q_{i}^{extra} / n\)       (13)

\(\Delta \varepsilon_{2}=(n-i) Q_{i}^{extra} / n\)       (14)

The energy described by functions (4) and (5) can be reached with just two switches working. The structure is simple in design and convenient in terms of control. In addition, it is easily expandable to different scales of series battery packs. Because of the similarity in the topology of the N-phase converters, the topology is further simplified as shown in Fig. 5. The combination of an equalizer and a switch array replaces the original multiple equalizers, simplifying the circuit and reducing the number of components in the system.

Fig. 5. Principle of the simplified equalization circuit. (a) Sharing equalization circuit. (b) When switch S_i-1 is closed. (c) When switch S_i is closed.

D. Overall Matrix Equalization Control

In general cell stacks, several cells are overcharged, while others are not. In addition, the two switching tubes in one equalizer have the opposite effect, and each equalization module only needs one switching to operate for equilibrium.

When the upper switch S_H in EC₁ is turned on, the battery B₁ transfers energy to the inductor L. Subsequently, the inductor L divides this energy among the remaining cells, where all of the remaining of the n-1 batteries absorbs 1 / (n-1) part of energy. When the upper switch S_H of the equalization module EC₂ is turned on, both of the batteries B₁ and B₂ transfer 1/2 part of the energy to the inductor. Then the inductor releases energy to the remaining batteries, which means the remaining n-2 batteries absorb 1/(n-2) part of the energy. These equalization modules consist of 2n-2 switching tubes and n-1 inductors. To further reduce the number of components, the simplified circuit described above can be adopted. However, this is done at the expense of the loss of equalization time.

Fig. 6. Interlaced converter energy transfer diagram.

When compared with natural equalization, the current hybrid control equalization is larger. This is due to the fact that the hybrid control equalization electromotive force is provided by the overcharged partial battery pack. However, the natural equalization electromotive force is provided by the energy difference between the two-part. When compared with forced equalization, the equalization current is the same. In the forced equalization control, the extra-energy is transferred one by one, which causes the upper and lower switchings of the equalization to serve the energy equalization process of different batteries. Up to one switching tube in the equalization module is working in hybrid equalization, which avoids the energy transfer effect from the repeated operation of the upper and lower switching tubes.

Initially, the SOC of all the batteries is measured to calculate SOC_ave. Equ. (15) gives the calculation method of the average power of the battery. Then the energy transfer matrix of the equalization module is multiplied by the time t to obtain the energy exchange amount after all of the batteries reach equilibrium, as shown in Equ. (16). The time matrix is solved by MATLAB to find the working time of each switch. A single-chip microcomputer is required to control the switch tube according to the time matrix reducing the energy circulation. This in turn, improves the working efficiency of the equalization circuit. The specific solution is introduced in the appendix.

\(Q_{\bar{B}}=\frac{\sum_{i=1}^{n} Q_{B_{i}}}{n}\)       (15)

\(\sum_{j=1}^{2 n-2} q_{j} t_{j}=\left[\begin{array}{c} Q_{B_{1}}-Q_{\bar{B}} \\ Q_{B_{2}}-Q_{\bar{B}} \\ \vdots \\ Q_{B_{i}}-Q_{\bar{B}} \\ \vdots \\ Q_{B_{n-1}}-Q_{\bar{B}} \\ Q_{B_{n}}-Q_{\bar{B}} \end{array}\right]\)       (16)

A block diagram of this system is shown in Fig. 7. This system was adopted to implement the charge balancing schemes. During the equalization process, the SOC is updated dynamically to be applied to the energy matrix. The latest solution is used to drive the equalization module again.

Fig. 7. Block diagram of the modulation scheme.

III. SIMULATION AND EXPERIMENTAL RESULTS ANALYSIS

A. Battery Modelling and Parameters Identification

The PNGV model is shown in Fig. 8 [20]-[22]. It has a higher precision and a more accurate description of the transient response process of a battery than the Thevenin model or the R_int model. In this model, U_OC stands for the ideal voltage source which is the same as the open circuit voltage of the battery; R₀ is the internal resistance of the battery; R_P is the polarization resistance; C_P is the polarization capacitance; I_P is the current on the polarization resistance; and C_B is the capacitance that describes the change in the open circuit voltage that accumulates.

Fig. 8. PNGV equivalent circuit model.

Available for the circuit diagrams C_B and C_P:

\(C_{b} \frac{\mathrm{d} U_{b}}{\mathrm{d} t}=I_{L}\)       (17)

\(C_{\mathrm{p}} \frac{\mathrm{d} U_{p}}{\mathrm{d} t}=I_{L}-\frac{U_{p}}{R_{p}}\)       (18)

According to Kirchhoff's voltage law, the open circuit voltage U_OC can be:

\(U_{OC}=U_{b}+U_{P}+I_{L} R_{0}+U_{L}\)       (19)

The equation of the state for building the PNGV model with the two capacitor voltages U_B and U_P is:

\(\left\{\begin{array}{l} {\left[\begin{array}{l} U_{\mathrm{b}} \\ U_{P} \end{array}\right]=\left(\begin{array}{cc} 0 & 0 \\ 0 & -\frac{1}{C_{P} R_{P}} \end{array}\right)=\left[\begin{array}{l} U_{\mathrm{b}} \\ U_{P} \end{array}\right]\left[\begin{array}{l} \frac{1}{C_{b}} \\ \frac{1}{C_{P}} \end{array}\right]\left[I_{L}\right]} \\ U_{L}=\begin{array}{ll} [-1,-1] {\left[\begin{array}{l} U_{\mathrm{b}} \\ U_{P} \end{array}\right]+\left[-R_{0}\right]\left[I_{L}\right]+\left[U_{o c}\right]} \end{array} \end{array}\right.\)       (20)

Where the two capacitor voltages act as state variables, and the battery terminal voltage acts as the output variable. The SOC, the criterion for achieving equalization, is not a directly measurable physical quantity. It is estimated by collecting the port voltage U_OC and the port current I_L, which are both measurable electrical parameters. A flow diagram of the system is depicted, as shown in Fig. 9.

Fig. 9. Block diagram of the system.

B. Analysis of Simulation Results

The balancing circuit and its working principle mentioned above, with the natural equalization control and the overall matrix equalization control, is proved respectively. A simulation model is built in PSIM in this section. This model includes a PNGV model and an experimental platform for four lithium-ion batteries.

In the experimental design, B₂ was initially overcharged (i=2, U_B2=4V, U_B1=U_B3=U_B4=3.6V). The working principle of balancing the energy of B₂ and the other cells is simulated and confirmed. The equalization circuit containing two batteries is equipped with one equalizer. Simulation experiments are demonstrated under both the natural equalization and overall matrix equalization control. The waveforms of the drive signal, current on inductor and voltage of battery in the four operating modes of the circuit simulation are shown in Fig. 10.

Fig. 10. Dynamic voltage waveform in forced equilibrium. (a) Key operation waveform in modes I and II. (b) Key operation waveform in modes III and IV.

The switch S_H2 has a conduction duty ratio of 50%. When the switch S_H2 is turned on, B₁ and B₂ transfer energy to the inductor. When the switch S_H2 is turned off, the inductor releases energy to B₃ and B₄. The switch S_L1 has a conduction duty ratio of one quarter. When the switch S_L1 is turned on, B₂, B₃ and B₄ transfer energy to the inductor. When the switch S_L1 is turned off, the inductor releases energy to B₁.

In the HNFABC, considering the overall balance of the battery pack, the working hours of each group of switch tubes are obtained based on the energy variation matrix. The drive circuit controls the operation of each switch tube. In any group of switch tubes, at most one switch is working to achieve balance, which avoids repeated energy exchange.

Fig. 11. Dynamic voltage waveform with the HNFABC.

C. The Analysis of Experiment Results

Simulation and experimental results prove the feasibility of the design proposed in this paper. The component parameters in the experiment are shown in Table III.

TABLE III SIMULATION AND EXPERIMENTAL SPECIFICATIONS

An experimental platform has been built in the laboratory to verify the feasibility of the proposed method as shown in Fig. 12. In order to make the effect more intuitive, B₁ is overcharged in the experiment. The goal is to transfer the excess energy of B₁ to B₂, B₃ and B₄ equally. In the equalization of four battery packs, the three equalizer modules include six switch tubes. The power transfer matrix of each switch tube is shown in equation (21).

\(q_{i, j}(p, u .)=\left[\begin{array}{rrr} -1 & -\frac{1}{2} & -\frac{1}{3} \\ -\frac{1}{3} & -\frac{1}{2} & -\frac{1}{3} \\ -\frac{1}{3} & \frac{1}{2} & -\frac{1}{3} \\ -\frac{1}{3} & \frac{1}{2} & 1 \end{array}\right]\)       (21)

Fig. 12. Experimental platform for testing.

To obtain the specific element value of the matrix:

\(I=\frac{D U}{L f}\)       (22)

where D is the duty cycle of the switch S_H; U is the voltage of the battery packs; L is the value of the inductor; and f is the frequency of the PWM. Calculating the energy storage according to the inductance yields the value of q in the matrix:

\(q_{(1,1)}=\int_{0}^{I} L i d i=\frac{1}{2} L I^{2}\)       (23)

In order to verify the above design, the simulation and experiment under charging, discharging and idle state are respectively shown in Fig. 13. The waveform of the experimental result has a good consistency with the waveform of the simulation result.

Fig. 13. Key waveforms of the simulation and experiment. (a) Simulation waveforms in the charging, idling and discharging states. (b) Experimental waveforms in the charging, idling and discharging state.

Simulation and experiment use the same component parameters and compare as much as possible in a similar condition. In the state of charging, discharging and idle, the average value of I_H is smaller than the average value of I_L, so that the energy of battery B_H is transferred to battery B_L. It’s clearly arrived at that according to the state of the switch in the simulation, the current waveform in the experiment is in good consistent with the waveform in the simulation.

D. Results Analysis

Four series battery packs set with the same parameters are balanced and compared under the following three control strategies.

1) Working Condition One: Natural Active Balancing Control. In the experiment, the average voltage of the battery was 3.7V, and the battery voltage gradient was set to 0.2V. The following working conditions are the same as above.

In the experiment, the battery voltage was collected every fifteen seconds, and the voltage change curve was plotted as shown in Fig. 14. It is concluded that the voltage does not cross the average value during the charge or discharge states, in which there is no repeated charge and discharge state. However, when the equalization is working, the voltage difference of the battery decreases and the energy transferred in one cycle is also reduced, which slows down the equalization speed.

Fig.14. Experimental results for natural active balancing control.

2) Working Condition Two: Forced Active Balancing control. As shown in Fig. 15, forced active balancing slightly increases the speed of equalization. However, the batteries are being repeatedly charged and discharged (both B₂ and B₃ are charged and then discharged), which accelerates battery aging.

Fig. 15. Experimental results for forced active balancing control.

3) Working Condition Three: Hybrid Naturally and Forced Active Balancing Control. As shown in Fig. 16, the equilibrium speed is constant without slowing down. The testing object is always in the state of charging or discharging (B₁ and B₂ are discharged, B₃ and B₄ are charged), without repeated charging and discharging, which reduces the damage to the battery.

Fig. 16. Experimental results for hybrid balancing control.

Compared with traditional circuits, the flexible interlaced converter has fewer components and lower voltage stress, which reduces the cost of the system and improves system stability. Deep analyses of the efficiency and power loss of the systems were performed as shown in Fig. 17.

Fig. 17. Power loss distributions in the experiment.

When the number of batteries increases, the energy and circuit losses transferred by the equalizer increase. However, the efficiency of the system increases slightly. This means that when the number of batteries is small, the advantages of the topology and its control method are not very obvious. However, with the further expansion of the equalization converter, the design reduces the characteristics of the battery so that it is repeatedly charged and discharged more prominently. By analyzing the energy loss of each part of the eight-cell series equalization, the main power loss of the system can be obtained by the switching and the inductor. Meanwhile, the application of low on-resistance SiC devices significantly reduces system losses in the future.

TABLE IV TYPICAL EQUALIZATION DEVICE COMPARISON

#1: flying-capacitor equalization topology; #2: multi- output winding transformer centralized equalization structure; #3: buck-boost centralized equalization structure; #4: flexible interlaced converter structure; #S: switch; #D: diode.

IV. CONCLUSIONS

In this paper the NHFABC strategy was proposed for a flexible battery energy balancing converter based on the PNGV model. The obtained analysis of experimental results concluded that the multiphase equalization converter with overall matrix equalization control achieved energy balancing, prolonged the service life of the battery stack, meanwhile reduced the energy loss in the equilibrium process. The main merit of this topology is that only half of the switches need to work to deliver excess power from the overcharged batteries to the other batteries, which avoids battery damage caused by repeated charge and discharge processes. According to the simulation results, this control strategy was shown to be more effective in the utilization of switches to enhance control performance when compared with traditional equalization control.

This paper presents a flexible interleaved converter and its control proposed which are suitable for the bidirectional power transfer applications in new energy electric vehicles. Future research will investigate the association between equalization efficiency and the coupling effect of inductors while using SiC devices. They will comprehensively analyze practical engineering problems, and reduce the power loss and volume of the passive devices.

APPENDIX