An ElectroStatic Discharge Algorithm for Electric Vehicle Li Ion Battery Parameters Estimation
Item Type Conference Paper
Authors Pervez, Imran;Antoniadis, Charalampos;Ghazzai, Hakim;Massoud, Yehia Mahmoud
Citation Pervez, I., Antoniadis, C., Ghazzai, H., & Massoud, Y. (2023).
An ElectroStatic Discharge Algorithm for Electric Vehicle Li Ion Battery Parameters Estimation. 2023 IEEE International Symposium on Circuits and Systems (ISCAS). https://
doi.org/10.1109/iscas46773.2023.10181565 Eprint version Post-print
DOI 10.1109/iscas46773.2023.10181565
Publisher IEEE
Rights This is an accepted manuscript version of a paper before final publisher editing and formatting. Archived with thanks to IEEE.
Download date 2023-11-29 21:09:09
Link to Item http://hdl.handle.net/10754/693184
An ElectroStatic Discharge Algorithm for Electric Vehicle Li Ion Battery Parameters Estimation
Imran Pervez, Charalampos Antoniadis, Hakim Ghazzai, and Yehia Massoud
Innovative Technologies Laboratories, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia Email:{imran.pervez, charalampos.antoniadis, hakim.ghazzai, yehia.massoud}@kaust.edu.sa
Abstract—This study proposes a new algorithm for param- eter estimation of the electric circuit model of Lithium (Li)- ion battery. The first-order battery-electric circuit model is considered in this work that resembles battery charging and discharging behaviors. The battery circuit element values have been modeled as polynomial equations with unknown coefficients.
An accurate estimation of the battery circuit element values is profound to accurately find the battery State of Charge (SoC), an immeasurable quantity required in battery management systems (BMS). The ElectroStatic discharge algorithm (ESDA) is used in this study to estimate the unknown polynomial coefficients and, in turn, the values of the battery circuit elements. The accuracy of the proposed ESDA in estimating the battery circuit element values is compared to the recently proposed Artificial Hum- mingbird Optimization Technique (AHOT), Chameleon Swarm Algorithm (CSA), and Tuna Swarm Optimization (TSO). The results demonstrate the superiority of the proposed algorithm for charging and discharging in battery parameters estimation over the other algorithms with an accuracy gain of at least 10%.
Index Terms—Electric vehicle, Battery, State of charge, Depth of discharge, charging and discharging rate, Nature inspired algorithm
I. INTRODUCTION
In order to satisfy the high energy demand, conventional sources of energy (e.g., fossil fuels) are used, which leads to CO2 emissions harmful to human health. This requires an urgent shift towards more sustainable forms of energy generation that help combat global warming. In order to achieve the sustainability goal, the energy generation trend is fiercely moving toward alternative energy generation and storage sources. The alternatives majorly include renewable electricity generation sources (e.g., photovoltaic, wind energy) in residential and commercial applications, while in the au- tomotive industry, the trend is to move to electric vehicles.
Electric vehicles (EVs) play a major role in reducing CO2 emissions by not only replacing conventional (fossil fuel- based) vehicles but also as energy storage devices supplying clean energy to the utility grid (vehicle-to-grid (V2G)).
The battery of an EV is instrumental in smooth operation for supplying and storing energy and thus needs to be highly efficient and reliable to fulfill storage and supply requirements.
Several types of batteries can be used for EV charging and discharging. Among these, lithium-ion (Li-ion) batteries owing to their high efficiency, long life, and high energy density, are becoming increasingly popular for EV operations [1], [2]. Due to their high adoption in EVs, the Li-ion batteries need to
be managed through a battery management system (BMS) to increase their lifespan [3]. However, the BMS requires correct information about the battery state of charge (SoC) that is not a measurable quantity [2], [4]. The battery SoC is also critical to enhancing the energy management strategy in EVs [5].
For these reasons, much research has been done to precisely measure battery SoC [6]. Several battery models (BMs) are available in the literature, such as the electrochemical model, the black-box model, and the electric circuit model [7], [8].
Electrochemical models are highly accurate but not very feasible due to their high complexity and the need for in- depth knowledge of chemical reactions and complex nonlinear differential equations [8], [9]. On the other hand, the black- box techniques, including Artificial Neural Network (ANN), fuzzy logic control (FLC), and Kalman Filters (KFs), require substantial calculations due to their complex implementation structures [7]. The electric circuit BM can clearly represent the EV battery characteristics [8], [10] - [12]. The parameter extraction for SoC estimation using these BMs are not com- plex compared to the models mentioned above. The simplest electric circuit BM can be represented as a voltage source in series with resistance [7], [12]. However, this model does not consider the SoC, Charging rate (Cr), and Discharging rate (Dr) of the battery [7]. Another BM that consists of an open-circuit voltage in series with a resistance and a parallel RC branch model the battery more accurately and considers the SoC, Cr, and Dr [7], [13]. The circuit elements of this model are represented through polynomial equations to approximate the behavior of experimental SoC. The parameter estimation problem thus becomes an optimization problem that minimizes the difference between the battery’s theoretical and experimental charging and discharging voltage.
Metaheuristic algorithms owing to their derivative-free global optimum convergence, are prevalent for this problem.
For instance, in [7], the authors compared four algorithms, namely the Differential Evolution (DE), Particle Swarm Opti- mization (PSO), Genetic Algorithm (GA), and Ageist Spider Monkey Optimization (ASMO) for first and second-order battery circuit models. The study found that DE outperformed all the first-order model algorithms while ASMO outperformed all algorithms for the second-order model. In [2], the Artificial Hummingbird Optimization Technique (AHOT) was proposed for battery parameter estimation. The algorithm relies on memorizing the location and pace of nectar replenishment of the food source the population of hummingbird is provided with. Also, remembering how long each food source remains
C R1
R2
Voc
Vthcci
Vdcj th
or
Fig. 1: First order RC circuit representing the battery model without being visited improves the searching capability for the optimum solution, thereby estimating the parameters accu- rately [2]. Moreover, the same study evaluated the performance of other very recent metaheuristic techniques like African Vultures Optimizer (AVO) [14], Jellyfish Search Optimizer (JSO) [15], Tuna Swarm Optimizer (TSO) [16], Arithmetic Optimizer (AO) [17], and Heap-based Optimizer (HO) [18].
All these techniques, except for AO, estimated the parameters accurately.
Although several algorithms are available in the literature with good estimation accuracy, there is a need for further improvement in the accuracy of battery parameters estimation to make the SoC estimation more accurate, thereby improving the expected reliability of the battery. Therefore, this study proposes a novel parameter estimation technique using the Electrostatic Discharge Algorithm (ESDA) to achieve this.
The parameters for both charging and discharging scenarios were estimated. The results proved the superiority of the proposed technique over recent techniques for battery param- eter estimation like AHOT [2] and TSO [16]. Moreover, we also compared the performance of the proposed algorithm over a recently proposed metaheuristic algorithm, namely the Chameleon Swarm Algorithm (CSA) [20] that was not used before for the battery parameter estimation.
The rest of the paper is structured as follows: Section II describes the battery circuit model. Section III explains the battery parameter estimation using ESDA. Section IV demon- strates the better accuracy in battery parameters estimation achieved with ESDA, and Section V concludes the study.
II. BATTERY CIRCUIT MODEL
The battery model developed in this study consists of an open circuit voltage source (Voc) in series with a resistance (R1) and a parallel RC branch (R2andC), as shown in Fig. 1.
These elements depend on the current SoC (SoCc), the current Depth of Discharge (DoDc), Cr, and Dr. The polynomial modeling of these elements in terms of SoCc, DoDc, Cr, and Dr, expresses non-linear behavior [8]. Following are the equations formulating the above elements as polynomial functions [8]:
R1= (c1+c2x+c3x2)e−c4y+ (c5+c6x+c7x2), (1) R2= (c8+c9x+c10x2)e−c11y+ (c12+c13x+c14x2), (2)
C=−(c15+c16x+c17x2)e−c18y+ (c19+c20x+c21x2), (3) Voc = (c22+c23x+c24x2)e−c25y+ (c26+c27y+c28y2
+c29y3)−c30x+c31x2,
(4) The above equations represent polynomial functions with 31 unknown coefficients (c1toc31). For the charging process, the parameters x and y in (1)-(4) are replaced by Cr and SoCc, respectively, while for the discharging process, they are substituted by Dr and 1 −DoDc, respectively. Thus, the battery output voltage for the charging and discharging case varies with different values of Cr and SoCc and Dr andDoDc, respectively. Finally, the battery output voltage is given by:
Vccthi = Qrc
C +iccR2
exp
−Tcc
R2C
+Voc−icc(R1+R2), (5) Vdcthi =
Qrc
C +idcR2
exp
−Tdc
R2C
+Voc−idc(R1+R2), (6) where Qrc denotes the battery remaining capacity, Tcc and icc are the charging time and current, respectively, while Tdc andidcare the discharging time and current, respectively. The ith charging voltage denotes the voltage value corresponding to ith experimental value of Cr and SoCc, while the jth discharging voltage denotes the voltage value corresponding tojthexperimental value ofDrandDoDc.
III. BATTERY PARAMETER ESTIMATION USING ELECTRO STATIC DISCHARGE ALGORITHM(ESDA) A. ESDA Algorithm
ESDA is a Nature Inspired (NI) algorithm proposed in [19]
that mimics the naturally occurring ElectroStatic Discharge (ESD) between different objects. The ESDA algorithm is designed to well manage the exploration of particles in the search space. The high exploration capability of ESDA helps exploring the search space thoroughly in order to reach the optimum solution as accurately as possible as will be described through its updating equations. ESDA starts by initializing objects (solutions) randomly in the search space as follows:
Y =
y11t y12t yt13. . . y1nt y21t y22t yt23. . . y2nt y31t y32t yt33. . . y3nt
. . . . . . . . . . . . ym1t ytm2 ym3t . . . ymnt
, (7)
subject to LB≤Y≤UB,
where the matrix Y has mparticles with ndimensions each distributed randomly within some lower and upper bounds (LBandU B respectively) that are problem specific.
In each iteration, three objects (particles are called as objects in ESDA) are chosen to be updated through ESD equations.
The object’s position update is done by knowing the number
of objects to be involved in ESD interaction which is done by comparing a random number between 0 and 1 by a constant value 0.5. Two objects are involved if the random number is greater than 0.5; otherwise all three are involved. For example, if two objects are involved in ESD interaction, the object’s position corresponding to the worst fitness value among the two objects (let us assume y2) is updated in terms of the better object among the two (let us assumey1) as follows:
yt+12 =yt2+ 2rand(yt1−yt2), (8) On the other hand, if all three objects are involved, the object’s position corresponding to the lowest fitness value (let us assume y3) is updated as follows:
y3t+1=yt3+ 2 rand1 (yt1−yt3) + 2rand2 (yt2−yt3), (9) where yt1, yt2, and yt3 denote the objects’ positions at the current iteration, y2t+1 and yt+13 correspond to the objects’
positions at the next iteration, and rand, rand1, and rand2
are uniformly generated random numbers between 0 and 1.
After objects’ locations update, any object falling out of the search space bounds or being updated more than three times is reinitialized randomly inside these bounds. The random reinitialization of an object involved in more than thre up- dates ensures high exploration. Moreover, for each location coordinate of the Objects that experienced less than three updates a random number is generated and compared with 0.2. The location coordinate for which the random number is less than 0.2 is reinitialized within its bounds which ensures further exploration for a specific location coordinate (dimension). The ESDA keep on exploring the search space through reinitialization while storing some non-reinitialized objects. This ensures a high diversification by comparing the reinitialized object’s fitness with the non-reinitialized object’s fitness thereby improving the accuracy of convergence.
B. ESDA for Battery Parameter Estimation
The difference between the theoretical charging (5) and discharging (6) voltage equations, and the corresponding ex- perimental battery voltage data for these equations has to be minimized. This is done by finding the polynomial coefficients of (5) and (6) that maximizes the inverse absolute error (IAE) of the difference between the theoretical and experimental voltages as follows:
argmax
x
1 1 +f it(x)
, (10)
wheref it(x)is the absolute difference between the theoretical and experimental voltage values defined as:
f it(x) =
Pn=N
n=1 |Vccth
i(x)−Vccex
i(x)| Pn=N
n=1 |Vdcth
i(x)−Vdcex
i(x)|
, (11)
where x is the vector containing the unknown polynomial coefficients and N is the number of experimental voltage values for charging and discharging cases. The algorithm starts spreading random objects (unknown coefficient sets with each
(a)
(b)
(c)
(d)
Fig. 2: Fitted curves for charging case for (a) CSA, (b) TSO, (c) AHOT, and (d) ESDA.
set containing randomly generated values of each coefficient) as in (7), and the fitness of each coefficient set is evaluated using (10). In this case, the number of dimensions n is 31 (31 unknown coefficients), while the number of particles m is 92 for the charging case and 150 for the discharging case (number of coefficient sets). Three coefficients sets (out of 92 or 150) are then chosen randomly to evaluate the type of ESD event (involving two or three objects). For two objects involved, the coefficient sets are updated using (8) while for three objects involved, they are updated using (9). Finally, any coefficient set with more than three ESD interactions (as explained in Section III.A) is reinitialized within the given bounds to help explore more possible values of coefficients within the search space for better accuracy of the IAE.
While for coefficient sets with less than three encounters, a component of an object (a coefficient of a coefficient set) is reinitialized through the random number generation procedure described in Section III.A again to add more exploration for a better accuracy. This process is repeated at every iteration until the total generation has reached. The total generation refers to the total number of function evaluations.
IV. RESULTS&DISCUSSION
In this section, the performance of the proposed ESDA is compared with the AHOT, CSA, and TSO in terms of convergence accuracy of Inverse Absolute Error (IAE) for battery charging and discharging cases. Moreover, the Sony US18650 battery with charge characteristics of 4.2V, 720mA,
TABLE I: Estimated polynomial coefficients for the charging and discharging cases for the proposed ESDA
Polynomial Coefficients (Charging)
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11
23.330 0.259 44.116 0.033 49.098 3.069 0.499 17.091 49.266 40.891 2.375
c12 c13 c14 c15 c16 c17 c18 c19 c20 c21 c22
18.858 12.177 17.919 2.482 0.044 13.537 0.273 3.258 0.221 9.322 7.202
c23 c24 c25 c26 c27 c28 c29 c30 c31 − −
12.626 42.357 0.032 39.862 1.06e-06 6.98e-06 1.51e-10 21.653 45.430 − − Polynomial Coefficients (Discharging)
c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11
0.056 1.420 0.485 0.253 0 0.348 2.635 3.461 0 0 0.338
c12 c13 c14 c15 c16 c17 c18 c19 c20 c21 c22
0 1.145 0 0 0 0 89.988 0 15.966 99.961 0
c23 c24 c25 c26 c27 c28 c29 c30 c31 − −
0.422 0 0.027 4.126 0.005 0 1.73e-07 0 0 − −
(a)
(b)
(c)
(d)
Fig. 3: Fitted curves for discharging case for (a) CSA, (b) TSO, (c) AHOT, and (d) ESDA
TABLE II: Inverse Absolute Error (IAE) for charging and discharging case for both algorithms
Algorithms
Difference in IAE with respect to ESDA (%) Charging Discharging
CSA 77.7 83.4
TSO 40 66.2
AHOT 7 17.9
ESDA 0 0
2.5h, 23◦C [21] was chosen to obtain the experimental charg- ing and discharging voltage values. Finally, we bounded the charging coefficients between 0 and 50 and the discharging coefficients between 0 and 100.
Table I summarizes the values for the unknown coefficients for charging and discharging cases evaluated through the proposed ESDA. Based on these coefficients, the curves for the charging and discharging cases of the ESDA are fitted to
approximate the experimental curve.
Figs. 2 and 3 illustrate the fitted curves for the charging and discharging cases respectively for all algorithms. Figs. 2(a)- (c) represent the fitted curves for CSA, TSO, and AHOT algorithms respectively for the charging case. The CSA and TSO algorithms do not fit well while AHOT fits better than both CSA and TSO . Fig. 2(d) represent the fitted curve for the proposed ESDA algorithm for the charging case. The proposed ESDA fitting is better than all the algorithms based on its per- centage increase in IAE values as shown in Table II. Though the ESDA fitting looks similar to the AHOT algorithm, its percentage increase in IAE over AHOT confirms its accuracy over AHOT. The better IAE value of the ESDA is a result of combined exploration action of or with location coordinate (each coefficient) random reinitialization. As explained previ- ously, the random reinitialization for coefficient sets (objects) with more than three updates help avoiding the less optimum regions along with maintaining high diversification as they are compared with the non-reinitialized coefficient sets. Moreover, to add some diversification in the non-reinitialized coefficient sets, the ESDA updates some coefficients from some randomly chosen coefficient sets. The high diversification leads to higher accuracy as evident in the results.
Similarly, Figs. 3(a)-(d) represent the fitted curves for CSA, TSO, AHOT, and proposed ESDA algorithms respectively for the discharging case. Again for this case, the higher IAE of the proposed algorithm in Table II proves the better fitting and accuracy of the ESDA over other algorithms. Despite the similarity in fitted curves of AHOT and ESDA, the higher IAE of ESDA proves its capability in modelling a more accurate battery model thereby serving to more accurate simulation applications requiring a battery model.
V. CONCLUSION
This paper proposed an Electro-Static Discharge Algorithm (ESDA) for estimating the battery circuit model parameters to theoretically estimate the battery state of charge. The battery was modeled through an electric circuit whose circuit elements were approximated as polynomial functions with unknown coefficients. The unknown coefficients were pre- cisely obtained using the proposed ESDA by minimizing the difference between the battery’s theoretical and experimental voltage output. The results demonstrated the superiority of the proposed technique over the AHOT, CSA, and TSO.
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