Modeling of Lithium-Ion Battery for Energy Storage ... - IEEE Xplore

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Abstract—Batteries are the power providers for almost all portable computing devices. They can also be used to build energy storage systems for large-scale ...
Modeling of Lithium-Ion Battery for Energy Storage System Simulation S.X. Chen, SMIEEE , K.J. Tseng, SrMIEEE and S.S. Choi, MIEEE Division of Power Engineering School of Electrical and Electronic Engineering Nanyang Technological University, Singapore [email protected], [email protected], [email protected] Abstract—Batteries are the power providers for almost all portable computing devices. They can also be used to build energy storage systems for large-scale power applications. In order to design battery systems for energy-optimal architectures and applications with maximized battery lifetime, system designers require computer aided design tools that can implement mathematical battery models, predict the battery behavior and thus help the designers search for the optimal schemes. This paper presentss a lithium-ion battery model which can be used on SIMPLORER software to simulate the behavior of the battery under dynamic conditions. Based on measured battery data, a mathematical model of the battery is developed which takes into account battery operating temperature and the rates of the battery charge/discharge currents. In addition, thermal characteristics of the battery are also studied.

are then compared with test results under various operating temperature, charge/discharge current rates conditions. II.

i(t) R2 V (t)

Keywords- Lithium-ion battery; dynamic model; energy storage system; SIMPLORER

I.

MODEL FORMULATION

The approach used here begins with the experimental data obtained from a ULTRALIFE UBBL10 lithium-ion battery. The data are expressed in terms of curves of battery terminal voltage during various constant-current discharge levels at different constant operating temperatures. A second set of data are the battery voltages following a step change of its current.

R1 E

Fig. 1. Equivalent circuit representation of lithium-ion battery

INTRODUCTION

In recent years, several approaches on energy storage for power systems have been studied intensely. For example, reference [1] describes the use of battery and hydrogen energy storage systems (ESS) in wind generation schemes. The storage systems are intended to achieve energy/power management of the renewable energy system. There are other forms of ESS, such as fuel cells, super-capacitors, compressed air energy storage, pumped storage and superconducting magnetic energy storage systems. Selection of suitable ESS is governed by several factors, including consideration on capacity, relative maturity of technology, cost, safety, environmental concern and performance. For some applications, lithium-ion (abbreviated Li-ion) batteries are suitable as ESS because of their high energy densities and long lifetimes. Moreover, lithium-ion is a low maintenance battery, an advantage that most other chemistries cannot claim. There is no memory effect, and no scheduled cycling is required to prolong the battery's life. In addition, the self-discharge is less than half compared to nickel-cadmium, making lithium-ion well suited for energy storage systems [2]. While detailed physics-based models have been built to study the internal dynamics of lithium-ion batteries [3]-[4], these models are not quite suitable for system-level design exercise. In this paper, a novel battery model suitable for system-level simulation is presented. The proposed model in terms of circuit representation is described first. Its mathematical equations are then presented and the model implementation in SIMPLORER is then described. Simulation results obtained from the model

To describe adequately the behavior of the battery under these operating conditions, the battery model should have two components: 1) An equilibrium potential E; 2) An internal resistance Rint having two components R1 and R2 The electrical schematic of these components is shown in Fig. 1. This proposed model extend that described in [5], in the terms of the new components included in Fig. 1. The roles of these components and the mathematical relations that describe each will be explained, as follows. A. Description of the Equilibrium Potential The equilibrium potential of the battery depends on the temperature and the amount of active material available in the electrodes. This can be specified in terms of the state of discharge (SOD) of the battery. In fact, in general the discharge capacity of the battery also depends on the discharge current, temperature and lifecycle. Thus it is necessary to seek a general expression for the potential E(t,T(t),i(t),l), where T(t) is battery temperature, i(t) is the discharge current and l is the lifecycle of the lithium-ion battery [5]. In view of the above, one can model the equilibrium potential E(t,T,i,l) based on experimental data, by 1) Firstly, arbitrarily chose a typical battery voltage vs SOD curve as a reference curve. The terminal voltage V(i,T,t,l) is

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then explained in terms of the battery SOD in a nth order polynomial. Also, from Fig. 1, the equilibrium potential E(t,T,i,l) is also seen as a function of V(i,T,t,l) and current i(t). These relationships are expressed as (1) and (2). 2) Secondly, the discharge rate and temperature corresponding to the reference curve are treated as the reference discharge rate and temperature. Therefore in view of the above, expressions for E, V(i,T,t,l), SOD and Rint are E[i (t ), T (t ), t , l ] = v[i (t ), T (t ), t , l ] + Rint ir (t )

(1)

n

k

v[i (t ), T (t ), t , l ] = ¦ ck SOD [i (t ), T (t ), t , l ] SOD[i (t ), T (t ), t , l ] =

Q

Rint = R1 + R2

t

³ i (t )dt

(3)

0

(4)

Where ck is the coefficient of the kth-order term in the polynomial representation of the reference curve and Qr is the battery capacity referred to the cutoff voltage for the reference curve. For k = 0, E = c0 is the open-circuit voltage at the beginning of discharge at the reference temperature of the reference curve. B. Description of the Internal Resistance Normally, the internal resistance Rint will increase with the state of discharge. In this model, Rint has two components R1 and R2. R1 is defined as the internal resistance of the lithiumion battery at SOD=0. It depends on the discharge condition, i.e. temperature, current level and lifecycle. R2 is the increase in Rint as SOD increases. R2 can also be affected by the temperature. However, it is proposed that an nth-order polynomial is used instead to describe the relationship between R2 and SOD. A correction factor Į(T) will then be used later to compensate for variation of R2 with T. Based on the above, R1 can be defined as a function of discharge current, temperature and lifecycle, as follows, R1 = f (i (t ), T (t ), l ) (5)

Take derivative on both sides of (5), δf δf δf ∂R1 = ∂i + ∂T + ∂l (6) δi δT δl R1 can be calculated by dividing the initial voltage drop (shown in Fig. 2) by the discharge current i(t) at SOD=0. From the

experimental

§ ∂i1 ¨ ¨ # ¨ ∂i n ©

∂T

16 15.5 15 0

0.1

T=25ć I=2 A

SOD 0.2

Fig. 2 Determination of the voltage drop at SOD=0 for different discharge condition

[ ∂R

1

∂R1

"

1

n

]

T

and

Then using least-square method to obtain the values δf δf δf of . Then R1 can be obtained as , , δ i δT δ l δf δf δf (i − iref ) + (T − Tref ) + (l − lref ) + R1 _ ref (8) R1 = δi δT δl where, iref, Tref, lref are the discharge rate, temperature and lifecycle of the reference curve. R1_ref is the internal resistance of the reference curve at SOD=0. Returning to R2, in general, R2 can be defined as a function of SOD and temperature, as follows: R2 = g (T (t ), SOD ) (9) Firstly choose another temperature discharge curve which is of the same discharge rate (the reference discharge rate). Then define i*R2_ref as the voltage drop (the difference between this curve and reference curve) at the same SOD, as for example shown in Fig. 3. The selection of the SOD point can be arbitrarily because as shown subsequently, it does not cause significant difference to the final simulation result. Normally, selection of the SOD point at the middle of these curves yields higher overall accuracy. An nth-order polynomial can be used to fit to that relationship between R2_ref and SOD. The same order polynomial as that with the potential E is recommended, again to yield higher accuracy. A correction term Į(T) is used to compensate for the variation of R2 at different discharge condition. This is illustrated as follows. The method to determine R2 is illustrated in Fig. 3, where experimental data from the ULTRALIFE UBBL10 lithium-ion battery is used. The reference curve and another curve at -20ć are chosen to calculate R2_ref, which is shown in Fig. 4. Then, n

R2 _ ref =

¦ r * SOD [i(t ), t ] k

k

(10)

k =0

∂l ·

1

1

¸ ¸ can be easily calculated. n ¸ ∂l ¹

# ∂T

data,

V

16.5

(2)

k =0

1

17

#

n

Expressed in matrix form, 1

1

ª ∂R1 º § ∂i « # »=¨ # « » ¨ n ¨ n ¬«∂R1 ¼» © ∂i

∂T

1

# ∂T

n

∂l

1

· ¸ ªδ f # ¸ «¬ δ i n ∂l ¸ ¹

δf

δf

δT

δl

º »¼

T

(7)

Fig. 3. Determination of the R2 for discharge condition at different temperatures.

In (10), rk is the coefficient of the kth order term in the polynomial representation of R2_ref. SOD selected is less than the SOD level at the termination of discharge. The terminal SOD chosen in this paper is 0.7. Then the correction term is i * R2 (T ) (11) α (T ) = i * R2 _ ref From (9)-(11), R2 of the internal resistance can be expressed as n

R2 = α (T ) * ¦ rk * SOD [i (t ), t ] k

(12)

k =0

(25° C) by setting a large cooling coefficient (hc = 100 W/m2 K). This simulates the idealized constant-temperature case. Comparison of the simulation and test results of discharge currents at 1 A and 4 A are shown in Fig. 5. As can be seen from the figure, a most satisfactory match between the model and test data has been obtained for the reference curve (2A) and while good agreement has also been obtained for all other discharge rates. TABLE I.

SPECIFICATIONS OF LITHIUM BATTERY TESTED IN THIS PAPER

Model Tested Type of Battery Operating Temperature Storage Temperature Range

Fig. 4. R2_ref for the lithium-ion battery based on the 25ćand 20ć curves. C. Description of the Thermal Characteristics Since E is temperature dependent, temperature must be calculated dynamically so that it is available for computation of E during each time step [6]. The temperature change of the battery is governed by the thermal energy balance [7] described byˈ dT (t ) 2 m * cp * = i (t ) * ( R1 + R2 ) − hc A[T (t ) − Ta ] (13) dt In (13), m is the battery mass (in kg), cp is the specific heat (J/kg/K), hc is the heat transfer coefficient (W/m2), A is the battery external surface area (m2), Tc is the ambient temperature. The heat power terms include resistive heating and heat exchange to the surroundings. Heat generation due to entropy change or phase change, changes in the heat capacity and mixing have all been ignored here because from [5], it has been concluded that such omission will not cause significant loss of model accuracy. D. Implementation based on the VHDL model in SIMPLORER Equations (1)-(4), (8), (12) and (13) provide complete description of the battery. From the derived mathematical model, the model can be simulated using VHDL-AMS method in SIMPLORER [8]. Unfortunately, lifecycle has not been considered in the battery model implementation since there is insufficient experimental data at the time of the writing of this paper. III.

UltraLife UBBL10 Cylindrical 18650 Li-ion cells assembly -32°C to 60°C -32°C to 60°C

Voltage

16.33 V

Capacity Heat capacity

6.2 Ah 925(J/kg/K)

Fig. 5. Simulation and test data at different current levels for the Ultralife UBBL10 lithium-ion batter The simulation data were processed to obtain the relation between the voltage and the SOD. The results are compared with the test data, as shown in Fig. 6. Again excellent match was achieved for the operating temperatures of -30ć and 60 ć.

COMPARISON OF SIMULATION AND TEST RESULTS

A. Discharge Characteristics A dynamic model of the ULTRALIFE UBBL10 lithiumion battery on the methodology given above was constructed for use in the SIMPLORER software. The parameters are given in TABLE 1. The rate dependence of potential was validated by testing the Ultralife UBBL10 lithium-ion VHDL model. The initial SOD is set to 0. The battery is maintained at room temperature

‹‰Ǥ͸Ǥ Simulation and test data at different temperature levels for the Ultralife UBBL10 lithium-ion battery

B. Charge Characteristics In this part of the study, the Ultralife UBBL10 lithium-ion battery was charged by a constant current 0.8A until the battery voltage reached 16.33V. Then the charging mode changed to constant voltage and the charge current eventually decayed to zero. This charging procedure is common, as can be seen in [9]. Fig. 7 shows the voltage increases during the charging operation. When the voltage reaches the maximum value of 16.34 V, it remains at this value. That is reasonable for the lithium-ion battery studied.

Fig. 7. Charging of the Ultralife UBBL10 lithium-ion battery: comparison between simulation and test results C. Thermal Characteristics In this part, the model is used to study how heat sink can affect battery operation. Using the same lithium-ion battery model written in VHDL-AMS with the initial SOD of the battery set to 0 and the load set to draw a constant current of 2 A, the heat transfer coefficient was varied. Fig. 8 shows the simulation results of the battery temperature during discharge under different cooling conditions. Notice that the final temperatures are 28.2°C (301.2°K) and 33.5°C (306.5°K) respectively for the constant cooling coefficients of 5 W/m2K and 1 W/m2K. The battery temperature is nearly equaled to the ambient (25°C) for very large cooling coefficients (hc = 100 W/m2K). From the simulation results, it can be concluded that the battery temperature increases faster when the constant cooling coefficient is lower.

IV.

A model of a lithium-ion battery suitable for energy storage application has been shown. The model was formulated in a general sense, but specifically for use in the SIMPLORER software. The method accounts for current rate- and temperature- dependence of the capacity and thermal dependence of the equilibrium potential. The modeling procedure, based on the experimental data, allows the model to have both good accuracy and the flexibility to represent other types of batteries. The mathematical description of the battery has been coded to a VHDL-AMS model in the SIMPLORER software. The battery model is shown to perform satisfactorily, up to the cutoff voltage. It is governed by the kth order term in the polynomial representation of the reference curve. Simulation results of the battery model agree well with the experimental data of an Ultralife UBBL10 lithium-ion battery in all static characteristics. This is because the internal resistance was defined based on the experimental data. It has two components R1 and R2. R1 is the initial resistance of the lithium-ion battery. It depends on the different discharge condition of temperatures, current levels and lifecycle. R2 is the increased resistance with the SOD. ACKNOWLEDGMENTS The authors would like to thank the technical staff of the Power Electronics and Drives Laboratory for the support given. Special thanks to Mdm Lee-Loh for her technical support in the equipment usage and software installation. Special thanks also go to D.L.Yao and T.D. Nguyen. REFERENCES [1]

[2] [3]

[4]

[5]

[6]

[7]

[8]

Fig. 8. Simulation results of battery temperature during discharge (2A, 25ć ambient) for different cooling conditions

CONCLUSIONS

[9]

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