# Modeling of Lead-Acid Battery Bank in the Energy Storage Systems

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2 Fig. 2 Suggested Battery model Fig. 1 Discharge curves of real ery [5] Some references represent the models which described eries dynamic behavior [6] [7] [8]. Battery model should track charging and discharging curves precisely. Representing model in [3] is static model with constant parameters that predict charge and discharge curves with one level of accuracy. The static voltage on ery (q), ery current (I ), state of charge (SOC), internal voltage (E in ) and terminal voltage (V ) equations represent as follow: Fig. 3 represents the resistance curve of ery which is the function of charging status. As is known, with the ery charging, its internal resistance is reduced. This non-linear curve is dependent on SOC and has been considered in the modeling of this article. Other environmental parameters affected in the model the eries. Parameters such as temperature, pressure, and ery age, but usually assumed to be standard conditions for the eries and therefore these parameters are not considered for simplification. dq I (2) dt q SOC 100 (3) Q E Q Q q Bq in E 0 K Ae (4) V E R I (5) in In these equations Q, E0, K, A, and B are constant which depend on ery type. The integral of current obtains the charges with the number between low limit of zero and high limit which determines by ery capacitance (Q). Fig. 2 shows the model of ery in simulation. In Figure 4, both voltage and resistance values are variable and are a function of the SOC. Voltage dependence of the SOC is determined by charge and discharge curves. Also, the ery internal resistance curve is given by the ery manufacturer. Fig. 3 Resistance curve based on the ery charge status III. BATTERY CHARGING Mainly lead-acid eries are charged in three ways: Constant Voltage, Constant Current, Combination of constant current and constant voltage In Combination of constant current and constant voltage, first method is used in beginning of the process and second method is used in end process. 933

3 In constant voltage method, constant voltage which is slightly more than the rated voltage, applied to ery. In this case, the charge current may be is too high in the beginning of the process and cause to reduce the ery life. In constant current method, ery charges with constant current which is selected in the range between 0.05C and 3C. Selected constant current depends on charge process speed which is needed. In the combination method, first ery charges with constant current and then charges with constant voltage. If the constant current value and constant voltage value are selected properly, this charging method can be optimum in term of adaptive objective function. Obviously combination method required more complex control structure. Fortunately lead-acid eries are less sensitive than charging current in compared with other eries. Due to low price of lead-acid eries in compared with others, these eries are charging with one of three methods unwary. In this paper ery charging simulation has been done with constant current method. IV. SIMULATION RESULTS The simulated ery bank contains 220 lead-acid eries which are connected in series. The capacity of each of them is the Q=500Ah and nominal voltage of total of them is 440 volts. The resistance of each ery in a complete charging state is R fc =0.006mΩ. The constant parameter of equation 4 is achieved as E0=488.7, K=24.2 and A=B=0 by predicting charging and discharging curves in figure 4. Simulated charging and discharging curves have been shown in figure 4. Figure 9 shows a real curve of coefficient of internal resistance of the ery and predicted one. The real curve has been shown with filled circle which is plotted by testing in the laboratory. The value of internal resistance of the ery is equal to resistance of ery in a fully charged state multiplied by the coefficient of internal resistance ( R R K ). As is clear value of internal f c r resistance of ery in discharged state is 4 times greater than its value in a fully charged state. For demonstrating the effect of this change in resistance and error caused by that it s enough if this value is multiplied by the number of eries, the resistance of each ery and charging current. According to the curve in figure 3, coefficient of internal resistance R versus state of charge SOC can be predicted by polynomial function. Regarding to the curve in figure 3 minimum degree of function for fitting is 3. Appropriate degree of predicted function of internal resistance of ery curve is 5 because of model accuracy and simplicity. This curve fitting is done by MATLAB. The third and fifth degrees of predicted functions are plotted in figure 5. Fig. 4 Charging and discharging curves of the ery bank Fig. 5 the predicted curves for R curve The effective value of error and total mean square errors of these fitted functions have been shown in table 1. The equation 6 shows the coefficients related to fifth degrees fitted function. 934

4 TABLE I FITNESS PROFILE OF PREDICTED FUNCTIONS Fitted function Effective error value Total mean square errors Third degree Fifth degree R R fc [( ( (67 10 ( 0.265) SOC 5.128] 3 5 ( (6) Fig. 7 Voltage of the ery bank R fc is resistance fully charged. Figure 4 shows the coefficient eries curve during the charging process. Battery voltage to the gassing voltage increases. After a jump start ery bank voltage gas that the charge should be stopped at this time. Subsequently, the voltage of the ery bank has a jump at this time should be to stop the charging process. Because extra charging ery caused the reduce ery life. As is clear in Figure 8, the initial charge of the ery bank is assumed 5%. Fig. 6 Internal resistance of the ery bank In figure 7 to 13, the charging process for the proposed model has been done. Figures 7 and 8 relating to the charging current is constant. Figure 7 voltage and figure 8 shows the ery bank charging. In this section, the constant current charge is equal to 0.1 C considered. Fig. 8 SOC of the ery bank Figures 9 and 10 relating to the charging voltage is constant. Figure 9 current and figure 10 shows the ery bank charging. In this section, the constant voltage charge is equal to 238 volt. 935

5 Fig. 9 Current of the ery bank Fig. 11 Current of the ery bank In Figure 9, it is clear that the constant voltage charging method, as the current decreases exponentially. Fig. 12 SOC of the ery bank Fig. 10 SOC of the ery bank Figures 11 to 13, the combination of constant current - constant voltage is shown. In this way, the eries are recharged with a constant current and after reaching the rated voltage, with voltage higher than rated voltage (slightly more) are charged. Figure 11 the charge current, Figure 12 state of charge and Figure 13 shows the voltage at the ery bank. This method is actually a combination of the two previous methods, which has more benefits compared to they are. In Figure 12 the initial state of charge the ery bank, 20% is assumed. From the Figures 4 and 8, can be understood that voltage for charging the ery bank, 5 and 20% respectively, 125 and 213 volts and they are quite in accordance with the ery manufacturer Curves. In Figure 14, curves are provided by the manufacturer that the ery is fully in accordance with simulation results. 936

6 REFERENCES Fig. 14 Voltage of the ery bank [1] Papi I, Simulation Model for Discharging a Lead-Acid Battery Energy Storage System for Load Leveling, IEEE Transactions on Energy Conversion, VOL. 21, NO. 2, Oct [2] Sitterly M, YiWang L, GeorgeYin G, Wang C., (2011) Enhanced Identification of Battery Models for Real-Time Battery Management, IEEE Transactions on Sustainable Energy, VOL. 2, NO. 3 [3] Chan H, Sutanto D., (2000) "A new ery model for use with ery energy storage systems and electric vehicles power systems", IEEE Power Engineering Society Winter Meeting, volume 1, No.1, pp [4] Salameh M, Casacca M, Lynch W. (1992) "A mathematical model for lead-acid eries", IEEE Transactions on Energy Conversion, volume 7, No. 1. [5] Technical Data LPL SERIES-Long Life Standby, LPL2-500 (2V500AH), Gita Battery. [6] Sitterly M, YiWang L, GeorgeYin G and Wang C., "Enhanced Identification of Battery Models for Real-Time Battery Managemen," IEEE Transactions On Sustainable Energy, Vol. 2, No. 3, July [7] Gould C and Bingham C. M., "New Battery Model and State-of- Health Determination Through Subspace Parameter Estimation and State-Observer Techniques," IEEE Transactions On Vehicular Technology, Vol. 58, No. 8, October [8] Zhang J, Song C, Sharif H and Alahmad M., "Modeling Discharge Behavior of Multicell Battery," IEEE Transactions On Energy Conversion, Vol. 25, No. 4, December Fig. 15 Current, voltage and SOC curve of the actual ery bank [7] V. CONCLUSION In this paper a new modeling was performed for a lead acid ery bank in the energy storage system. In most modeling related Lead-acid eries, internal resistance, considered to be fixed. In an energy storage system, a huge bank of eries may be composed from the large number (About several hundred eries) of eries. In this case, the fixed internal resistance of eries is something wrong. Hence, in this paper for modeling the ery bank, this resistance is considered a variable. Internal resistance of the ery depends on the state of charge that in modeling, the ery manufacturer's data, has been considered. Simulation results and conform it to ery manufacturer's catalogue, Represents the correctness the modeling has been presented. 937

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