An improved equalization circuit with bidirectional CUK converter for series-connected battery strings

This paper proposed an improved equalization circuit based on a bidirectional CUK converter. Compared with traditional bus equalization circuits based on CUK converter, it owns a simpler structure with fewer inductors, resulting in a smaller volume and higher energy density of the proposed equalization circuit. The operation principle and steady-state characteristic of the equalizer are analysed. The equalizer is applied to the energy balance of the series-connected battery strings, and the balance principle is designed. The proposed equalization system achieves a fast energy balance of the battery pack. Simulation results verify the effectiveness of the designed equalization circuit and balance strategy.


Introduction
The lithium-ion battery has the advantages of a wide operating temperature range, high energy density, long cycle life, low self-discharge rate, and no memory effect [1] .In most applications, lithium-ion batteries are used in series.However, some lithium batteries in the battery pack will be overcharged or over-discharged.Overcharging or over-discharging will have an irreversible impact on the performance and life of a single lithium battery and the series-connected battery strings [2] .By utilizing an equalization circuit, the power of each single lithium-ion battery can be regulated at the same level.
Dissipative equalization circuits directly dissipate excess energy on power resistors or switching components, resulting in low efficiency and energy waste [3] .To save energy, non-dissipative equalization circuits are widely researched.Furthermore, the bus-based equalization circuits [4][5][6][7] are proposed, which improve the balancing speed.The equalization speed can be significantly improved through the point-to-point equalization of lithium-ion batteries at the same time.However, the hardware circuit of the bus-based equalization is complex, resulting in disadvantages of weight.
This paper proposed an improved equalization circuit based on a bidirectional CUK converter, which has a simpler structure with fewer capacitors than a traditional bus equalization circuit based on a bidirectional CUK converter.Thus, it has the advantages of smaller volume and higher energy density.Additionally, the proposed equalization circuit can achieve energy transfer between batteries with odd serial numbers and batteries with even serial numbers simultaneously, and the fast-balancing speed in series-connected battery strings can be achieved.Simulation results verify the effectiveness of the designed equalization circuit and balance principle.

Circuit configuration
The structure of the designed improved equalization circuit is shown in Figure 1(b).The seriesconnected battery strings consist of m batteries with odd serial numbers and n batteries with even serial numbers.The number of inductors is half compared with Figure 1(a) [5]  .According to the voltage of the batteries, the equivalent circuit is shown in Figure 2. The critical characteristics of the proposed equalization circuit are as follows: • The circuit corresponding to any battery with an odd serial number and the circuit corresponding to any even serial number constitute a complete CUK converter.• The switch signals of the batteries with odd and even serial numbers participating in equalization are complementary.The switches of the stationary batteries keep off.• In each equalization cycle, the batteries participating in equalization need to contain odd and even serial numbers.The equalization target is to make the batteries' voltage consistent.( )

Operation modes
where UBp is the voltage of battery BRgt_p.ILx is the average current of iLx.The relationship between equalization current and equalization voltage can be described as: (2) According to Equation (2), on the equalization circuit on the left side, the equalization current positively correlates with the battery voltage.On the equalization on the right side, the equalization current is negatively correlated with the battery voltage.

Equalization strategy design
The equalization strategy based on eight batteries is designed to achieve battery energy equalization.
Step 1: We sort the batteries according to their voltage.We calculate the average value of battery voltages Uav and set the average voltage error band Uav±δ.
Step 2: For the batteries with odd serial numbers, we calculate the average values of battery voltages above the Uav+δ and below the Uav-δ, named Uodd-ab and Uodd-be, respectively.The same operation is implemented in the batteries with even serial numbers, named Ueven-ab and Ueven-be.
Step 3: We calculate the difference ΔU1 between the Uodd-ab and Ueven-be and the difference ΔU2 between the Ueven-ab and Uodd-be.If ΔU1>ΔU2, the batteries with odd serial numbers and whose voltages are above the Uav+δ will output energy, and the batteries with even serial numbers and whose voltages are below the Uav-δ will input energy.If ΔU1<ΔU2, the batteries with even serial numbers and whose voltages are above the Uav+δ will output energy, and the batteries with odd serial numbers and whose voltages are below the Uav-δ will input energy.
Step 4: In the equalization process, the PI controller controls the absolute maximum inductor current to iLref.

Simulation results
The proposed improved equalization circuit is verified by simulation with eight batteries.To observe the charge and discharge of the batteries conveniently, the current flow direction from the battery is selected as the positive direction in the simulation.The parameters are listed in Table 1.
Time(s)  The equalization current waveforms are illustrated in Figure 5.The initial battery voltages UB1-UB8 are 3.3 V, 3.2 V, 3.1 V, 3.0 V, 2.9 V, 2.8 V, 2.7 V, 2.6 V, and 2.5 V, respectively.According to Figure 5, the 1 st , 3 rd , 6 th and 8 th batteries participate in equalization.The 1 st and 3 rd batteries output energy and the 6 th and 8 th batteries input energy.The simulation result shows that the equalization currents of the 1 st and 3 rd batteries are positively correlated with the battery's voltages, and the equalization currents 6 th and 8 th batteries are negatively correlated with the battery's voltages.
Figure 6 illustrates the battery's voltages variation curve in equalization.Considering the simulation duration, the initial battery voltages UB1-UB8 are 3.576 V, 3.564 V, 3.547 V, 3.570 V, 3.593 V, 3.526 V, 3.577 V, and 3.562 V, respectively.The average voltage error band is Uav±3 mV.Obviously, after equalization, the batteries voltages UB1-UB8 are 3.5648 V, 3.5628 V, 3.5594 V, 3.5629 V, 3.5648 V, 3.5594 V, 3.5648 V, 3.5604 V, respectively.The maximum voltage difference of the battery pack is balanced to within 5.4 mV, which meets the requirements.And it verifies the feasibility and effectiveness of the equalization circuit proposed in this paper.

Conclusion
This paper presented an improved equalization circuit based on a bidirectional CUK converter.Due to the fewer inductors, the circuit can easily achieve smaller volumes and higher energy density.The circuit configuration and operation modes are described, along with the relationship between equalization current and equalization voltage.Moreover, the paper designs the equalization strategy based on the proposed equalization circuit.The proposed equalization system achieves a fast energy balance of seriesconnected battery strings.

Figure 1 .Figure 2 .
Figure 1.Traditional bus equalization circuit-based on bidirectional CUK converter (a) and improved equalization circuit based on CUK converter (b).

Figure 4 .Mode 1 :
Figure 3. Equivalent circuit in Mode 1.Figure 4. Equivalent circuit in Mode 2. Mode 1: The switches SLf_i-SLf_j on the left side are on, the SRgt_p-SRgt_q on the left side are off, and the other switches keep off.The equivalent circuit is shown in Figure 3.The direction of the current is marked.CLf is equivalent to isolated capacitors on the left side.UCf and iCf are the voltage and current of CLf, respectively.CRgt_x is the equivalent capacitor of isolated capacitors of the x th battery on the right side.Mode 2: The state of switches on the left and right sides is contrary to Mode 1.The other switches keep off.The equivalent circuit is shown in Figure 4. CRt is equivalent to isolated capacitors on the right side.UCr and iCr are the voltage and current of CRt, respectively.CLf_x is the equivalent capacitor of isolated capacitors of the x th battery on the left side.iLx is the xth battery inductor current, and UCx is the x th series capacitors CLf_x1 and CLf_x2 voltage, or CRgt_x1 and CRgt_x2 voltage.RC_x is the equivalent series resistance of CRgt_x or CLf_x, and RL_x is the equivalent series resistance of LRgt_x or LLf_x.In Mode 1, the batteries BLf_i-BLf_j charge corresponding the inductors LLf_i-LLf_j, the equivalent capacitors CLf and CRgt_p-CRgt_q charge the inductors LRgt_p-LRgt_q and batteries BRgt_p-BRgt_q.The differential equations are obtained by KCL and KVL laws as follows: Similarly, we analyze the charge balance of the capacitors in the right side in a switching cycle.The following relationship can be found.

Figure 5 .
Figure 5. Equalization current waveforms in the equalization process.