Dynamic charge equalisation for series-connected batteries

Transcription

1 Dynamic charge equalisation for series-connected batteries C.S. Moo, Y.C. Hsieh, I.S. Tsai and J.C. Cheng Abstract: A charge equalisation circuit is proposed for the series-connected battery bank in a serial charging scheme. The charge equalisation is based on buck boost conversion, and hence is essentially nondissipative. The subcircuit associated with each battery acts as a current diverter to transfer the excess charging current from the fully charged batteries to the flat ones. By dynamic redistribution of charging energy, charge equalisation can be achieved more quickly and efficiently. The applicability of this approach is confirmed by experiments. 1. Introduction With increasing concern about air pollution, especially in urban areas, CO 2 emission from automobiles is considered to be a major cause. Therefore cars that use non-fossil fuels are at an advantage, and electric vehicles (EVs) form the most established and important alternative. Electric vehicles are usually powered by rechargeable secondary batteries, more specifically, by a bank of series-connected batteries because the required voltages of EVs are generally much higher than the voltage level of a single battery [1]. Since batteries play an important role in EVs, efficient and harmless battery charging is a major research issue. Efficient charging reduces charging time and extends the vehicle mileage, while harmless charging prolongs battery cycle life and achieves lower battery operating cost. For convenience, the batteries in the bank are treated as a whole and therefore have to be charged in series by a single power source. Due to complicated electrochemical reactions, battery performance is very sensitive to the environmental temperature, the charging/discharge profile, and the state of charge (SOC). In practice, it s difficult to make all conditions identical for all the batteries under operation. Consequently, the restored capacities of the batteries in a bank may not be the same during the charge/discharge process even though the same current flows through each battery. The ends of the charging and discharging processes become indefinite due to imbalance among the batteries. If the charging process is not well controlled, some batteries may be excessively refilled while others may not be charged sufficiently. On the other hand, some batteries may be excessively discharged at the end of an operating cycle. The imbalance tends to be magnified through repeated charging and discharging. r IEE, 23 IEE Proceedings online no doi:1.149/ip-epa:23661 Paper first received 15th January 23 and in revised form 9th May 23. Originally published online: 24th July 23 C.S. Moo, I.S. Tsai and J.C. Cheng are with the Power Electronics Laboratory, Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung, Taiwan, 4, R.O.C Y.C. Hsieh is with the Department of Electrical Engineering, Kao-Yuan Institute of Technology, Kaohsiung County, Taiwan, 21, R.O.C Studies concerning the battery life suffering from unbalanced charging have been conducted [2]. To prolong the battery cycle life and improve charging efficiency, it is recommended that all batteries in the bank should be equally charged before ending the charging process. Many techniques have been developed for charge equalisation. Switched capacitors are used in [3] to transfer charges among unbalanced batteries. In [4, 5] a transformer with multiple output windings is adopted to provide the same charging voltage on each battery. Alternatively, charge equalisation can be effectively executed by utilising a set of power converters, or a power converter with multiple outputs, to recirculate the excess energy to the common bus or other batteries [6 ]. A charge equalisation circuit for balance charging is proposed which makes use of buck boost converters in a simple configuration and is essentially nondissipative. The batteries are dynamically balanced by transferring the excess energy from the fuller batteries to the other empty ones. This performs charge equalisation more efficiently with less circuit losses. All the battery voltages are monitored and the charge equalisation mechanism is applied throughout the entire charging process. The control algorithm is implemented digitally with a single chip microprocessor to achieve flexibility and extendibility. 2 Circuit operation Figure 1 shows the proposed charge-equalising circuit. The battery bank with N batteries connected in series is charged by a single power source. The main charger is represented by a constant-current source. Each battery in the seriesconnected battery bank is shunted with a charge equalisation subcircuit. The subcircuits are basically buck boost converters. All the subcircuits are identical to each other except the subcircuit M 1 associated with the battery.the subcircuits M 2 to M N are activated to divert the excessive energy from the corresponding batteries to the upstream batteries, while M 1 diverts the excessive current into the downstream batteries. The operation of the charge equalisation circuit is described by two illustrative cases. Figure 2 shows the case of activating the bottom subcircuit M N. During the turn-on period of, the buck boost converter draws a current from battery to the inductor.when is turned off, the current in flows through the upstream batteries IEE Proc.-Electr. Power Appl., Vol. 15, No. 5, September 23 51

2 subcircuit M 1 subcircuit M 2 subcircuit M N a control Fig. 1 Charge equalisation circuit b Fig. 3 Operation modes of activating subcircuit M 1 a turns on b turns off a V gn D n T s i Ln i Sn V B b Fig. 2 Operation modes of activating subcircuit M N a turns on b turns off i B i B(n-1),,y 1. In this transfer process, energy is taken from, which has greater restored energy, and redistributed to other batteries. The redistribution of energy reduces the differences of SOC among the batteries. The operation of subcircuits M 2 to M N 1 is similar to that of M N, while the power-transfer path of M 1 is different from the others. Figure 3 shows the operation of subcircuit M 1. Once the active power switch in the subcircuit M 1 is turned on, M 1 withdraws current from the battery, and then transfers it to the downstream batteries when is turned off. Figure 4 shows the relevant waveforms of the charge equalisation circuit. In the illustrated case, the seriesconnected batteries are charged by a constant current, Fig. 4 T s Schematic waveforms of charge equalisation subcircuit and one of the subcircuits M n is activated. To reduce the switching losses of the active power switches, all the subcircuits are operated in discontinuous current mode (DCM). With DCM operation, the active power switches suffer only one battery voltage when being switched off. Generally the voltage difference among batteries will be within a small range as compared with the nominal battery voltage. Hence, a unified voltage level V B is specified for all batteries in the circuit analysis. 52 IEE Proc.-Electr. Power Appl., Vol. 15, No. 5, September 23

3 During the turn-on interval, the corresponding active power switch S n draws a current from the battery to the inductor. The inductor current increases linearly and reaches its peak at the instant of switching off S n i sn ¼ V B L t; t D n T s ð1þ i sn ¼ ; D n T s ot T s where T s is the switching period and D n is duty ratio of M n. With buck boost conversion, only the rising part of the inductor current is carried by S n. The average current I dis,n dispensed from the battery in one switching cycle can be expressed as I dis;n ¼ 1 Z i sn dt ¼ V B n T s ð2þ T s T s 2L When S n is turned off the inductor current decreases linearly. The decreasing rate depends on the voltage imposed on it. For the subcircuits M 2 to M N the voltages are the summations of the upstream batteries. On the other hand, the serial voltage of the downstream batteries is imposed on the inductor if M 1 is activated. Then the average current released from an activated subcircuit M n can be expressed as < : I rel;n ¼ 1 2 V B L D n V BD n T s ðn 1ÞV B ¼ V B n T s 2Lðn 1Þ n 6¼ 1 I rel;n ¼ V T s 2LðN 1Þ n ¼ 1 ð3þ SOC measured value curve fit Fig. 5 Measured relationship between SOC and battery loaded voltages wait for T vdp start charge for n = 1 to N read battery voltage V n Consequently, for a battery, B m the total current obtained from other activated subcircuits can be obtained as >< I obt;m ¼ I rel;1 þ i¼2 PN i¼mþ1 I rel;i m 6¼ 1 >: I obt;m ¼ PN I rel;i m ¼ 1 ð4þ voltage detecting phase for all n V n = V full? No calculate SOC by battery voltages calculate duty ratio of each module terminate charge 3 Control algorithm The charge equalisation circuit is controlled by a pulsewidth-modulation (PWM) controller which is digitally implemented with a single-chip microprocessor. Even though the open-circuit voltage method is more precise as an indication of the SOC of a battery [9], it is not applicable to real-time applications. To estimate the SOC of a battery when being charged, the loaded voltage method is adopted. The relationship between the load voltage and the SOC is shown in Fig. 5. The battery was repeatedly charged and rested to measure the loaded voltage and the open-circuit voltage, i.e. SOC, respectively. This relationship depends on the battery type. For most batteries, the relationship between the loaded voltage and the SOC can be well fitted by a second-degree polynomial equation. In the illustrative case, the equation can be expressed as S ¼ :241 V 2 þ 7:21 V 53: ð5þ where S is the SOC and V is the loaded battery voltage. As charging proceeds, the loaded voltages of the batteries are sequentially monitored via a multiplexer and then transformed into digital signals by an analogue-to-digital converter. These digital signals are translated into SOC by (5). The control algorithm of the microprocessor is explained by the flow chart in Fig. 6. Each control cycle is divided into two phases, the voltage-detecting phase and the chargeequalisation phase, lasting for durations T vdp and T cep, charge equalisation phase Fig. 6 Control flow chart reset t a for activated modules, process PWM signals t a < T cep? respectively. During the voltage-detecting phase, all subcircuits stop. Only the charging current from the main charger flows through the battery bank. All the battery voltages are detected and the duty ratios for the activated subcircuits calculated. In the charge- equalisation phase the active power switches of the subcircuits are operated with the duty ratios calculated in the previous voltage-detecting phase. The charging currents injected into batteries in this phase are with abrupt change and are different to each other. Therefore the battery voltage cannot be an applicable index for estimating the SOC of the batteries. During the voltage-detecting phase all batteries are equally charged by a current. Due to the inertia of battery reactions, the battery voltages become stable after a period of constant-current charging. The measuring of battery voltages should be executed as late as possible. For this reason, the controller idles for a period T vdp, and measures the battery voltage at the end of the voltage-detecting phase. By transforming the battery voltages measured at the end of the no IEE Proc.-Electr. Power Appl., Vol. 15, No. 5, September 23 53

4 voltage-detecting phase to SOC, the restored capacity Q est,n for each battery B n can be estimated. During the charge-equalisation phase the injected charge from the main charger into each battery is T cep.tomake therestoredcapacityoneachbatteryequalattheendof charge-equalisation phase, the target equalised charge Q tar should be: Q tar ¼ T cep þ 1 N X N n¼1 Q est;n ð6þ As indicated in (3) and (4), the charge transferences between activated subcircuits and other batteries are mutually influenced. Therefore the charge to be given or received cannot be calculated by a plain equation. The Gauss Seidel iteration method is applied to solve this problem [1]. The expected restored capacity Q n canbecalculatedas Q n ¼ Q est;n þði obt;n I dis;n þ ÞT cep ð7þ The control objective is to make the restored capacity of each battery equal to Q tar, that is, (6) and (7) should be equal. By substituting (2) (4) into (6) and (7), the duty ratio settings can be obtained. D n ¼f n ð ; D nþ1 ; ; Þ¼ D2 1 N 1 # þ XN i i 1 þ 2LðQ 1=2 n 6¼ 1 >< est;n Q tar þ T cep Þ V i¼nþ1 B T s T cep D n ¼f n ð ; D 3 ; ; Þ " # ¼ XN i i 1 þ 2LðQ 1=2 est;1 Q tar þ T cep Þ n ¼ 1 >: V i¼2 B T s T cep ðþ The iteration procedure is illustrated by Fig. 7. By (), the Gauss Seidel iteration method is applied to solve the duty ratio of each subcircuit, until the maximum duty ratio () () () = = = DN = (k) (k 1) (k 1) (k 1) = f 1 (, D3,,DN ) deviation between two subsequent steps is smaller than the preset threshold, e. 4 Experimental results A laboratory circuit for charge equalisation was built to verify the applicability of the proposed approach. The battery bank to be charged consists of four series-connected batteries. The primary parameters are listed in Table 1. In applications where a higher voltage with more seriesconnected batteries is required, a multiplexer with more input ports is necessary for monitoring battery voltages. Table 1: Primary parameters Battery capacity C Charging current Switching period T s Full battery loadedvoltage V full Nominal loaded voltage V B Balance charging period T cep Voltage detecting period T vdp Inductance L n 4Ah Figures and 9 show the waveforms of battery currents for two operating cases. In Fig., the subcircuit M 3 is activated. When the switch S 3 is turned on, the current flowing into battery B 3 declines linearly. The upstream batteries and are excessively injected when S 3 is turned off. Figure 9 shows the case that subcircuits M 2 and M 4 are operated with the duty ratios of.4 and.2, respectively. An experiment of balance charging was carried out by deliberately setting the batteries at different SOC. At the beginning, the loaded voltages from to B 4 are 12.7, 13.53, 13.11, and V, respectively. Figure 1 shows the continuously recorded battery voltages. During the chargeequalisation phases, the battery voltages fluctuate drastically and the battery currents differ from each other. During the voltage-detecting phases, all batteries are charged by the same charging current. Figure 11 depicts the loaded voltages at the ends of these phases. All the voltages come up to their final values with slight differences. This indicates that they have approximately the same SOC. 2A 1 ms 14.5 V 14 V 3 s 3 s 5 mh n = N down to 2 (k) (k ) (k) (k) D n = f n (, Dn +1,, ) i B1 1 no n = 1 to N (k) (k 1) D n Dn max < ε? current, 5A/div i B2 2 3 i B3 end i B4 time, 2μs/div 4 Fig. 7 Iteration procedure to solve duty ratios of subcircuits Fig. Battery currents when M 3 is activated 54 IEE Proc.-Electr. Power Appl., Vol. 15, No. 5, September 23

5 current, 5A/div i B1 i B2 i B3 i B V B1 V B2 V B3 V B charging time, min Fig. 11 Battery voltages at end of voltage-detecting phases Fig time, 2μs/div Battery currents when M 2 and M 4 are activated V B1 V B2 V B3 V B4 The charge equalisation circuit makes use of DC DC buck boost conversion, which is simpler than the previous nondissipative approaches. All buck boost converters in the charge equalisation circuits are operated under a battery voltage. With such a low voltage stress on circuit components the circuit losses can be greatly reduced. The charge equalisation circuit is composed of the corresponding number of subcircuits. Except for the topmost one, all the subcircuits are identical; therefore it is easy to extend the battery number in the bank Fig charging time, min Continuously recorded battery voltages 5 Conclusions Charge equalisation is a major issue in charging seriesconnected batteries. It concerns the efficiency of the charging process and the prolongation of battery lifetime. A balance charging technique has been proposed for this purpose. The proposed circuit performs charge equalisation dynamically, and thus can reach the balanced state more efficiently. The control can be executed offline or dynamically over the charging period. This will make the batteries reach charge equalisation earlier, or at least decrease the differences in SOC. Experimental results manifest the effectiveness of this circuit. 6 References 1 Chan, C.C., and Chau, K.T.: An overview of electric vehicles challenges and opportunities. Proc. 22nd Int. Conf. on Industrial electronics, control, and instrumentation, (IECON), Taipei, Taiwan, August 1996, pp West, S., and Krein, P.T.: Equalization of valve-regulated lead-acid batteries: issues and life test results. Proc. 22nd Int. Conf. on Telecommunication energy (INTELEC), Phoenix, AZ, September 2, pp Pascual, C., and Krein, P.T.: Switched-capacitor system for automatic series battery equalization. Proc. 12th Conf. on Applied power electronics (APEC), Atlanta, GE, February 1997, pp Sakamoto, H., Murata, K., Sakai, E., Nishijima, K., Harada, K., Taniguchi, S., Yamasaki, K., and Ariyoshi, G.: Balanced charging of series connected battery cells. Proc. 2th Int. Conf. on Telecommunication energy (INTELEC), San Francisco, CA, October 199, pp Kutkut, N.H., Wiegman, H.L.N., Divan, D.M., and Novotny, D.W.: Design considerations for charge equalization of an electric vehicle battery system, IEEE Trans. Ind. Appl., 1999, 35, (1), pp Hung, S.T., Hopkins, D.C., and Mosling, C.R.: Extension of battery life via charge equalization control, IEEE Trans. Ind. Electron., 1993, 4, (1), pp Hopkins, D.C., Mosling, C.R., and Hung, S.T.: Dynamic equalization during charging of serial energy storage elements, IEEE Trans. Ind. Appl., 1993, 29, (2), pp Kutkut, N.H.: A modular nondissipative current diverter for EV battery charge equalization. Proc. 13th Conf. on Applied power electronics (APEC), Anaheim, CA, February 199, pp Aylor, J.H., Thieme, A., and Johnson, B.W.: A battery state-ofcharge indicator for electric wheelchairs, IEEE Trans. Ind. Electron., 1992, 39, (5) 1 Saadat, H.: Power system analysis (McGraw-Hill, 1999) IEE Proc.-Electr. Power Appl., Vol. 15, No. 5, September 23 55