Hybrid Sinusoidal-Pulse Charging Method for the Li-Ion Batteries in Electric Vehicle Applications Based on AC Impedance Analysis

Abstract

A hybrid sinusoidal-pulse current (HSPC) charging method for the Li-ion batteries in electric vehicle applications is proposed in this paper. The HSPC charging method is based on the Li-ion battery ac-impedance spectrum analysis, while taking into account the high power requirement and system integration. The proposed HSPC method overcomes the power limitation in the sinusoidal ripple current (SRC) charging method. The charger shares the power devices in the motor inverter for hardware cost saving. Phase shifting in multiple pulse currents is employed to generate a high frequency multilevel charging current. Simulation and experimental results show that the proposed HSPC method improves the charger efficiency related to the hardware and the battery energy transfer efficiency.

I. INTRODUCTION

Li-ion batteries are widely used in energy storage systems (ESS) owing to their high energy density, good cycle-life performance, and low self-discharge rate. Battery chargers and their corresponding charging methods are conceived as a bridge for the electricity and chemical energy transformation in ESS. They both affect the system performance [1], [2] including the charging speed, cycle life, system efficiency, etc. Many charging methods have been discussed in the literature, such as constant-current (CC) charging, constant-voltage (CV) charging [3], and pulse charging (PC). Among them, the CC and CV are the most extensively used. However, the polarization effect and diffusion limitation of distribute more uniformly. However, the effect of periodic pulse profiles on the overall performance of systems is still vague when compared with CC with the same mean current lithium ions in fast charging applications degrade their performance [4], [5]. Pulse charging (PC) provides a rest period for the ions to diffuse and for the electrolyte ions to [6], [7]. Other charging techniques are proposed to obtain better battery charging performance. These include fuzzy control, neural network, and gray prediction [8]-[10]. However, the circuit design of such charging systems is found to be complicated and expensive.

Battery chargers, as the charging executors in ESS, have also been studied extensively to achieve higher efficiency, compact structure and easy integration [11]-[13]. Numerous assessments have been carried out to improve the charger efficiency through soft switching [14], [15], auxiliary circuits [16], hybrid topology, etc. [17].

In addition to hardware efficiency, the energy transfer efficiency of a battery is also important to an ESS. The energy transfer efficiency is the ratio of the charging and discharging capacity in the electrochemical reaction cycle of a battery. Recently, a sinusoidal ripple current (SRC) charging method has been proposed as a feasible solution for better charging performance with minimum battery ac impedance Zmin [18], [19]. The experimental results in [18] show that, compared with the conventional CC charging method, the charging time, energy transfer efficiency, maximum rising temperature, and lifetime of the Li-ion battery in the SRC test have been improved by about 17%, 1.9%, 45.8%, and 16.1%, respectively.

However, further improvements are still required before implementing the SRC into practice. First, the generator of the high rate-high frequency sinusoid charging current lacks detail. A dual active bridge is proposed in [20] to output a sinusoid charging current. However, the charging frequency is fixed instinctively at two times the line voltage frequency. That is not able to achieve the minimum ac impedance Zmin for a Li-ion battery. A sinusoid charging current of 1kHz with an average current of 1.5A is generated in [18]. However, the charger efficiency is neglected. In addition, the above method is not flexible enough to integrate with existing vehicle on-board systems. Finally, the impact of charging frequency variations of Zmin is not clear.

This paper focuses on improving the overall efficiency of ESSs by a combination of the minimum-ac-impedance theory in SRC and power electronics charging technology. The effectiveness of the proposed method is experimentally compared with that of the SRC, PC and CC methods.

 

II. AC-IMPEDANCE CHARACTERISTIC OF LI-ION BATTERIES AND ENERGY TRANSFER EFFICIENCY

Fig. 1 shows a Li-ion battery ac-impedance model. Assuming that the charging frequency is fs, the ac impedance of the battery can be written as (1) [18], [21], and [22]:

Fig. 1.Li-ion battery ac impedance model.

where Rct is the transfer resistance, Cd represents the double layer capacitance, Ro is the ohmic resistance, and Ld is the anode inductance. The frequency fZmin that corresponds to the minimum ac impedance Zmin is:

As shown in Fig. 1, the frequency for the minimum impedance can be utilized to reduce the energy loss in the battery charging process, which leads to the maximum energy transfer efficiency (the optimal electrochemical reaction) [23]-[25]. Here, the energy transfer efficiency is expressed as:

where Qdischarge/Qcharge is the discharging/charging capacity, Idischarge/Icharge represents the discharging/charging current, and Tdischarge/Tcharge means the discharging/charging time.

 

III. PRINCIPLE OF THE HYBRID SINUSOIDAL-PULSE CHARGING METHOD BASED ON THE AC IMPEDANCE CHARACTERISTIC

In this section, an ac impedance characteristic test for Li-ion batteries is presented. It is performed by an ac impedance analyzer CHI650E as shown in Fig. 2. To avoid the capacity error caused by the activation effect of a virgin li-ion battery, the test battery is extracted from a cycled battery package. Fig. 3 shows the ac-impedance spectrum test results. Some data are presented in TABLE I, where the minimum-ac-impedance frequency fZmin and the minimum ac impedance Zmin are 2.3kHz and 0.316Ω, respectively.

Fig. 2.Ac-impedance analyzer.

Fig. 3.Measured ac impedance spectrum of a Li-ion Battery.

TABLE IAC IMPEDANCE RESULT BY BATTERY-CHARGING TEST

As shown in Fig. 3, the curve of |Zbattery| is flat within the frequency domain where Zmin exist. The |Zbattery| varies within 1.5% from fZmin /4 to 4fZmin. Therefore, multiple currents with frequencies around fZmin can also be utilized to achieve the energy transfer efficiency improvement, due to the impendence reduction.

A multilevel current source is used for the multiple frequencies charging the current generation, as shown in Fig. 4. It is composed of three parallel boost circuits. The inductors L1, L2, and L3 can be inductors or motor stator windings. Based on the experimental tests and data in [18], a frequency range of 3-5 kHz matches the traction application switching frequencies. This implies the HSPC generator can share the switches in a three phase traction inverter. The device S1, S2, and S3 are the switching devices in the lower bridge arm of a three phase inverter, and D1, D2, and D3 utilize the anti-parallel diode of the upper bridge arm. In forming three boost converters, the dc source voltage must be less than the battery package voltage on the board.

Fig. 4.Schematic of proposed charging circuit.

In Fig. 5 the duty cycle of any output current iDx in one boost unit is 1-D, where D represents the duty cycle for Sx, assuming a continuous inductor current. For the symmetrical distribution of iDx in ich, the time shift between iD1 and iD2 is Δt12 and is equal to The time shift between iD1 and iD3 is Δt13 and is equal to Since 0 < Δt12 < Δt13 < (1 - D)Ts, the duty cycle limit can be deduced as D<0.6.

Fig. 5.Waveform of driving signal and current.

Fig. 5 shows the operation of a circuit with D=½. ug1 - ug3 are the driving signals for the switche S1 - S3. iD1 - iD3 are the currents through diodes D1 - D3. The switches S2, and S3 have a phase shift of 360°×½×⅓=60° and 360°×½×⅔=120° to S1, respectively. There are six sequential operation modes in one cycle, as shown in Fig. 6.

Fig. 6.Operation modes of the proposed battery charging circuit.

Mode 1[t0-t1]: Switches S1 and S2 are in the on-state, and S3 is turned on at t0. L1-S1, L2-S2, and L3-S3 conduct current, as shown in Fig. 6(a). The battery charging current ich is zero.

Mode 2[t1-t2]: At t1, switch S1 is turned off, and the current in S1 flows through L1-D1 to charge the battery. The battery charging current is the same as the current through L1, as shown in Fig. 6(b).

Mode 3[t2-t3]: At t2, switch S2 is turned off. L1-D1, L2-D2, and L3-S3 conduct current. As shown in Fig. 6(c), the battery charging current is the sum of the currents in L1 and L2.

Mode 4[t3-t4]: At t3, switch S3 is turned off. L1-D1, L2-D2, and L3-D3 conduct current. As shown in Fig. 6(d), the charging current is the sum of the currents in L1, L2 and L3.

Mode 5[t4-t5]: At t4, switch S1 is turned on. As shown in Fig. 6(e), which is similar to mode 3, the battery charging current is the sum of the currents in L2 and L3.

Mode 6[t5-t6]: At t5, switch S2 is turned on. As shown in Fig. 6(f), which is similar to mode 3, the battery charging current is equivalent to the current in L3.

Then, the system returns to mode 1 to start a new cycle. The switching frequency of each bridge device is equal to the desired charging frequency, that is, f-Zmin.

Fig. 6 shows that with a phase-shifting of 60°, the output forms a multilevel charging current similar to the voltage from a multilevel voltage inverter. The switch operates in a chopping mode which is different from the constant current region operation in [18]. Therefore, the power loss in a device can be reduced. The duty cycle and switching frequency of each boost leg is adjusted to regulate the charging current. The proposed circuit can be extended to an N phase topology with multiple inductors or windings, like a multi-phase motor. Then switch Si+1 has a phase delay of compared to switch Si, 1 ≤ i ≤ N. The PC charging method can also be performed with a zero phase delay.

 

IV. SYSTEM DESIGN AND CONTROL SCHEME

As mentioned in section III, the devices in HSPC can be shared with the switching devices and the anti-parallel diode in three phase traction inverters. Here, the inductance value in the system design is discussed based on the output current waveform analysis.

The output current waveform iDx in one boost unit is shown in Fig. 7, using iD2 as an example. When S2 is turned off, the D2 current is equal to the inductor current, with an average IL. The current ripple of iD2 is expressed in (4). Thus, the actual diode D2 current from to can be obtained by (5):

where Vin is the input voltage and L is the inductance value of L2. The fundamental component of iD2 can be derived as iω(t) in (6):

Fig. 7.Analysis of the output current iDx in one boost unit.

Since iD1 and iD3 have phase shifts of with respect to iD2, the fundamental wave total charging current is as equation (9):

From (7-9), b1 is more complicated than a1 for the fundamental wave estimation. In fact, a1 presents the fundamental component of IL in (5), and b1 presents the fundamental component of ΔiD2 in (5), which is smaller than a1. Thus, to achieve a better fundamental wave estimation, L need to be designed to decrease b1 in (9). A close loop based on (7) is demonstrated in Fig. 8.

Fig. 8.Control scheme of proposed system.

In Fig. 8, the average current regulator can be an ac/dc or dc/dc converter to perform the current regulation and electric isolation. vin can be regulated by the PI controller of IL in the current regulator voltage loop. The system command is calculated by the average charge current command

The HSPC generator aims at charging current shaping through duty cycle D adjustment. The relationship between the current total harmonic distortion (THD) in HSPC and D is analyzed in the Appendix. The effectiveness of the control method above is demonstrated in Fig. 9.

Fig. 9.Close-loop control performance (simulation).

The average inductor current IL follows the system command through Vin well. The peak value estimation in (9) is well matched with the envelope of Iω in the charging current, and the fundamental charging current estimation is verified.

 

V. CHARGER EFFICIENCY COMPARISON

As discussed in previous sections, the charging efficiency is defined by the charger efficiency and the energy transfer efficiency. In this section, the charger efficiencies of HSPC and SRC are compared.

First, the SRC and HSPC charging methods are assessed by LTSPICE to get the power loss without a heat sink or cooling system. The schematic of the SRC charger and its closed-loop control circuit is shown in Fig. 10.

Fig. 10.Schematic of SRC charging circuit.

As shown in Fig. 10, a dc voltage source is selected as the battery load and a MOSFET IRF840 is used, which enables the reference to the switching device and experimental test in [18]. The spice IRF840 model was provided by the device manufacturer. The current peak-peak value is 4.4A and the average is 2.2A as shown in Fig. 11. The output current is 2.3kHz and the power loss in the device increases with a increasing output current, as shown in Fig. 12.

Fig. 11.Simulation waveform of the charging current in SRC (a) and (b) HSPC.

Fig. 12.Power loss and Vds on MOSFET with different average currents.

The results in Fig. 12 are calculated according to (11):

where Ich is the average value of the charging current, VR1 is the voltage in the current sampling resistor R1, Vds is the MOSFET voltage, and Ebattery is the battery terminal voltage. As shown in (11), the efficiency is dominated by the ratio between Vds and Ebattery. Ebattery rises slightly following the charging current, while Vds increases significantly due to the constant current region requirement. Thus, the power loss increased significantly with the charging current, as shown in Fig. 12. The power loss increment is 20W when the charging current increases from 0.5C to 1C, during which the charger efficiency falls from 30% to 17%.

The power loss on the device of the HSPC is calculated with the same average current and switching devices, as shown in Fig. 13. Only the MOSFET power loss is considered while the losses in the inductor and diode are not included. The square symbol means the power loss in a single MOSFET while the circle symbol represents the charger efficiency including three MOSFETs. The power loss is much smaller when compared with Fig. 12. The efficiency varies from 79% to 90% depending on the charging current.

Fig. 13.Power loss in switching device with different charging current value.

Next, the output current harmonic characteristic of the HSPC is compared with the SRC and pulse current (PC) charging methods. The PC duty ratio is 50% and the frequency is the same as for the HSPC.

The FFT results of both output currents are shown in Fig. 14. The average current is the same but the harmonics of the PC over 10kHz are much higher than the HSPC. The RMS currents of the PC, SRC and HSPC are 3.11A, 2.69A and 2.57A, respectively. Therefore, the power loss in R0 caused by the pulse is 1.46 times that of the HSPC, causing an additional temperature rise.

Fig. 14.FFT analysis of the charging current in SRC,HSPC and PC.

 

VI. ENERGY TRANSFER EFFICIENCY COMPARISON

In this section the energy transfer efficiency is tested experimentally for the HSPC, PC, SRC and CC.

Fig. 15 shows the battery-charging energy transfer test platform that comprises battery test equipment, an SRC charger, and a charger that can perform the HSPC and PC functions. The inductors L1, L2, and L3 are manufactured with different values, i.e. 2.5mH, 2.4mH, and 4mH, for inductance variation consideration in the motor windings. The battery test equipment can perform CC charge method, and the temperature rising for all four of the tests is saved to a data recorder. The charging frequency of the HSPC, PC and SRC are all set in 2.3kHz.The average current is 2.2A. Fig. 16 shows the generated SRC, HSPC and PC charging currents, and all of the tests are carried on the same battery.

Fig. 15.Battery test platform.

Fig. 16.Charging current waveform of SRC, HSPC and PC.

Fig. 16 shows the results from the HSPC and SRC methods. The charger can output HSPC current under the asymmetric bridges inductance situation. The temperature rising and charging efficiency are shown in Fig. 17 and Fig. 18. The temperature rising in Fig. 17 shows that the CC has the minimum charging temperature rising. The rise in the SRC and HSPC are similar. The PC has the maximum temperature rising, which corresponds to the charging current RMS calculation in section V.

Fig. 17.Temperature rising comparison of four charging method.

Fig. 18.Energy transfer efficiency comparison.

Fig.18 compares the energy transfer efficiency of the four charging methods. The proposed HSPC and the SRC have the best performance in energy transfer efficiency, while the PC has the lowest efficiency.

 

VII. CONCLUSION

In this paper, a hybrid sinusoidal-pulse-current charging method (HSPC) was proposed and tested for the Li-ion batteries in electric vehicle applications. The proposed topology consisted of three parallel connected boost circuits. This method is based on the ac-impedance spectrum and aims at high power requirements and vehicle power train system integration. The proposed method was compared with the SRC, PC and CC methods. It was established that the charger efficiency and energy transfer efficiency in a battery can be improved with the HSPC, resulting in a higher system level efficiency. The application of this method can be extended to other battery types, for example, lead-acid batteries.