Modeling, dynamics, and control of electrified vehicles

Thus estimation methodsbased on battery models are developed broadly.The remainder of this chapter is organized as follows:Section 1.2duces several kinds of modeling approaches for Li-io

Modeling, Dynamics, and Control of

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Dongpu Cao, and Haiping Du

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1 Modeling, Evaluation, and State Estimation for Batteries 1

Hao Mu and Rui Xiong

3 HESS and Its Application in Series Hybrid Electric Vehicles 77

Shuo Zhang and Rui Xiong

3.2 Modeling and Application of HESS 80

4 Transmission Architecture and Topology Design of EVs and HEVs 121

Jibin Hu, Jun Ni and Zengxiong Peng

4.2 EV and HEV Architecture Representation 125 4.3 Topology Design of Power-Split HEV 129 4.4 Topology Design of Transmission for Parallel Hybrid EVs 143

v

5 Energy Management of Hybrid Electric Vehicles 159

Hong Wang, Yanjun Huang, Hongwen He, Chen Lv, Wei Liu

and Amir Khajepour

6 Structure Optimization and Generalized Dynamics Control

Liang Li, Sixiong You, Xiangyu Wang and Chao Yang

6.3 Extended High-Efficiency Area Model 212

Xiaoyuan Zhu and Fei Meng

Chen Lv, Hong Wang and Dongpu Cao

8.2 Brake-Blending System Modeling 278 8.3 Regenerative Braking Energy-Management Strategy 283 8.4 Dynamic Brake-Blending Control Algorithm 292

References 306

Yafei Wang and Hiroshi Fujimoto

9.5 Riding and Energy Efficiency Control 332

Brett McAulay, Boyuan Li, Philip Commins and Haiping Du

12.2 System Modeling and Problem Formulation 411 12.3 Fault-Tolerant Tracking Controller Design 418

13 Integrated System Design and Energy Management of Plug-In

14.3 Formulation of Cost-Optimal Control Problem 483

CHAPTER 1

Modeling, Evaluation, and State Estimation for Batteries

Hao Mu and Rui Xiong

Beijing Institute of Technology, Beijing, China

1.1 INTRODUCTION

Currently, hybrid electric vehicles (HEVs) and electric vehicles (EVs)promise a future of green travel in which fuel-consuming engines arereplaced with electric motors, thus reducing our dependence on fossilenergy and ultimately producing less harmful emissions Such vehicles can

be plugged in at home overnight or at the office or in a parking spaceduring the day, using electricity that is generated at a centralized powerstation or even by renewable sources The key component to the achieve-ment of these electrical systems is the energy storage system, namely, thebattery technology

The lithium-ion (Li-ion) battery, as depicted in Fig 1.1, is the mostcommon choice for phone communication and portable appliancesbecause of its many advantages, such as high energy-to-weight andpower-to-weight ratios (180 Wh/kg and 1500 W/kg, respectively) andlow self-discharge rate (Linden and Reddy, 2002; Capasso and Veneri,

2014) In addition, among all rechargeable electrochemical systems,Li-ion technology is the first-choice candidate as a power source forHEVs/EVs However, this technology is still delicate and affected bynumerous limitations, such as issues of safety (Doughty and Roth, 2012),cost (Lajunen and Suomela, 2012), recycling (Gaines, 2011), and charginginfrastructure (Veneri et al., 2012)

To ensure the power battery works safely and reliably, which is a tion of the battery management system (BMS), the temperature, voltage,and current of the batteries should be monitored and the states of the bat-teries should be estimated precisely in real time (Junping et al., 2009; He

of batteries, like the state of charge (SoC), state of health (SoH), and state

of function (SoF) directly due to the complicated electrochemical process

1

Modeling, Dynamics, and Control of Electrified Vehicles Copyright © 2018 Elsevier Inc.

and various factors in practical applications Thus estimation methodsbased on battery models are developed broadly.

The remainder of this chapter is organized as follows:Section 1.2duces several kinds of modeling approaches for Li-ion batteries, such asphysical-based models, equivalent circuit models (ECMs), etc In

indispens-able for battery research Then, considering the popularity of differentmodels, the ECMs are selected to illustrate parameter identification meth-ods, which can be divided into offline and online ones according to real-time capability Due to the balance problem between model accuracy andthe computation burden of the BMS, an evaluation criterion is introduced

to determine the optimal number of RC networks in the models

batteries, in particular about SoC estimation Many SoC estimation ods will be classified systematically and the multiscale adaptive extendedKalman filter (MAEKF) algorithm for state and parameter collaborativeestimation will be elaborated on since it is not only provides satisfactoryestimation accuracy, but also low computation burden Some conclusionsare drawn inSection 1.5and references are listed in references section

meth-1.2 BATTERY MODELING

Many battery models, which are lumped models with relatively few meters, have been put forward especially for the purpose of vehicle powermanagement control and BMS development The most commonly usedmodels can be categorized as electrochemical models and ECMs (Plett,2004a; He et al., 2011a, 2011b; Vasebi et al., 2007; Zhu et al., 2011;

utilize a set of coupled nonlinear differential equations to describe the

Figure 1.1 Different types of Li-ion batteries.

pertinent transport, thermodynamic, and kinetic phenomena occurring inthe cell They can translate the distributions into easily measurable quanti-ties such as cell current and voltage and build a relationship between themicroscopic quantities, such as electrode and interfacial microstructureand the fundamental electrochemical studies and cell performance.However, they typically deploy partial differential equations (PDEs) with

a large number of unknown parameters, which often leads to large ory requirements and heavy computation burdens, so the electrochemicalbattery models are not desirable for BMSs (Smith et al., 2010) The sim-plified electrochemical models, which ignore the thermodynamic andquantum effects, are proposed to simulate the electrochemical and voltageperformance The Shepherd model, the Unnewehr universal model, theNernst model, and the combined model are the typical choices Theequivalent circuit battery models are developed by using resistors, capaci-tors, and voltage sources to form a circuit network Typically, a big capac-itor or an ideal voltage source is selected to describe the open-circuitvoltage (OCV); the remainder of the circuit simulates the battery’s inter-nal resistance and relaxation effects such as dynamic terminal voltage TheRint model, the Thevenin model, the DP model, and their revisions arewidely used

mem-1.2.1 Physical-Based Models

Electrochemical models usually use coupled nonlinear PDEs to describeion transport phenomena and electrochemical reactions to achieve highaccuracy, but incur heavy computation load For instance, a pseudo two-dimensional (P2D) model, developed by Doyle et al (1993), is one of themost popular variants and can take seconds to minutes to simulate

a single particle model (SPM) that assumes electrodes are represented bytwo single spherical particles To improve the accuracy of the SPM underhigh C-rate, several extended single particle models (E-SPMs) have beenproposed (Luo et al., 2013; Schmidt et al., 2010; Khaleghi Rahimian

electrolyte are taken into account In general, electrochemical modelssuch as P2Ds, SPMs, and E-SPMs are more accurate than ECMs, butrequire a large number of immeasurable parameters, leading to overfitting

in parametric identification Therefore the pursuit for battery modelswith high accuracy and computational efficiency still remains a challenge

3

Modeling, Evaluation, and State Estimation for Batteries

Although electrochemical battery models are suitable for ing the electrochemical reactions inside the battery, their complexity oftenleads to the need for more memory and computational effort Thus theymay not be practical in the fast computation and real-time implementa-tions needed for EV BMS This problem has been addressed by manyresearchers by investigating reduced-order models (ROMs) that predictthe battery behavior with varying degrees of fidelity (Smith et al., 2008,

understand-2010) To reduce the order of an electrochemical battery model, zation techniques can be applied to retain only the most significantdynamics of the full-order model (Tanim et al., 2015) Various discretiza-tion techniques are utilized to simplify the full model’s PDEs into a set ofODEs of the ROM while keeping the fundamental governing electro-chemical equations InShi et al., 2011, six different discretization meth-ods (listed in Table 3) are addressed and compared for battery systemmodeling

discreti-1.2.1.1 Single Particle Model

The SPM assumes a single electrode particle in each electrode and gible electrolyte diffusion Conservation of Li1 species in a single spheri-cal active material particle is described by Fick’s law of diffusion:

particles occupying electrode volume fractionεs, as5 3εs/Rs The linearizedButlere
Volmer electrochemical kinetics and is given by

where i0 is the exchange current density, R is the universal gas constant,

T is the temperature, and αaand αc are the anodic and cathodic transfercoefficients, respectively

1.2.1.2 Pseudo Two-Dimensional Model

The P2D model, as depicted in Fig 1.2, is constructed based on theassumption that electrodes are seen as an aggregation of spherical particles(2D representation) in which the Li1 ions are inserted The first spatialdimension of this model, represented by variable x, is the horizontal axis.The second spatial dimension is the particle radius r The cell is

Figure 1.2 Systematic chart of P2D model.

5

Modeling, Evaluation, and State Estimation for Batteries

comprised of three regions that imply four distinct boundaries The cific descriptions of this model can be found inSabatier et al (2015).

spe-1.2.2 Lumped Parameter Electric Model

The complexity of the electrochemical models and limitations of thecomputers in the past led researchers to investigate another modelingapproach called electrical circuit modeling or equivalent circuit (EC)modeling Today, for many applications, it is important to strike a balancebetween model complexity and accuracy so that the models can beembedded in microprocessors and provide accurate results in real-time(Pattipati et al., 2011) In other words, it is important to have models thatare accurate enough, and not unnecessarily complicated EC modeling isone of the most common battery modeling approaches especially for EVapplications Having less complexity, these models have been used in awide range of applications and for various types of batteries (Marc et al.,

con-structed by putting resistors, capacitors, and voltage sources in a circuit.The simplest form of an EC battery model is the internal resistancemodel (Johnson, 2002) The model consists of an ideal voltage source Uocand a resistance Ro Adding one RC network to the internal resistancemodel can increase its accuracy by considering the polarization character-istics of a battery Such models are called “Thevenin” models (Salameh

Figure 1.3 Schematic of Thevenin model.

et al., 1992) and are illustrated inFig 1.3; in this figure, Utis the battery’sterminal voltage, Uocis the OCV, ILis the load current, Ro is the internalresistance, Rp and Cp are equivalent polarization resistance and capaci-tance, respectively.

Adding more RC networks to the battery model may improve itsaccuracy but it increases the complexity too Thus a compromise isneeded when computational effort and time are vital This subject is dis-cussed in more detail in the following sections

Recently, fractional order models (FOMs) have attracted increasinginterest in the field of electrochemical energy storage systems One of

and performed time-domain parametric identification with theLevenberge
Marquardt algorithm, but fixed the differentiation orders

at 0.5 and 1 through the estimation study Xu et al (2013) presented afractional Kalman filter for SoC estimation based on a FOM, wherethe differentiation order of the Warburg element was also fixed at 0.5,and the other model parameters were identified based on a single pulseresponse The fixing of differentiation orders helps to reduce the diffi-culty of parametric identification, but also significantly limits themodel accuracy

One common EC model used in EIS tests was proposed by JohnEdward Brough Randles in 1947 The model, called Randles circuitmodel, is illustrated in Fig 1.4 In cell modeling using the EIS method,

Figure 1.4 Randle circuit.

7

Modeling, Evaluation, and State Estimation for Batteries

each component of the electrical circuit model is related to an chemical process in the cell.

electro-In this model, Ro is the ohmic resistance, the pseudo RC network isused to simulate the charge transfer process and double layer effect, andthe Warburg impedance is used to describe the diffusion phenomenon ofions in solid phase In actual applications, due to the capacitance disper-sion, the Warburg impedance can be expressed in s-domain as:

where ZW denotes the impedance, WD is the coefficient, α is the order

to evaluate capacitance dispersion (0# α # 1), and when α 5 0 is theresistance,α 5 1 is the capacitor

1.3 EVALUATION OF MODEL ACCURACY

1.3.1 Some Experiments

1.3.1.1 OCV Test

The OCV is a measure of the electromotive force (EMF) of the battery,which is known to have a monotonic relationship with the SoC of thebattery

Existing OCV modeling approaches can be broadly classified intochemistry-based and current
voltage based approaches In chemistry-based approaches, the OCV of each electrode (anode and cathode w.r.t.some reference) is expressed as a function of the utilization of the elec-trode (the lithium concentration in the electrode normalized by the maxi-mum possible concentration) or the SoC of each electrode It is generallyassumed that this anode and cathode SoC varies linearly with the cellSoC Subsequently, the difference between the OCV of the anode andcathode gives the OCV of the complete cell High current rates (i.e., nearthe rated maximum) have been shown to affect the macroscopic processes

in a way that the OCV hysteresis vanishes for Li-ion cells, which regularlyshow OCV hysteresis after low current application Roscher et al con-ducted OCV (full and partial charge-discharge cycle) tests on Li-ionphosphate (LiFePO4) batteries to characterize the hysteresis and recoveryeffects The final OCV model is constructed by concatenating the actualSoC, the recovery factor, and the hysteresis factor

The current
voltage based OCV
SoC characterization can besummed up in two simple steps:

1 Collect pairs of {OCV, SoC} values, spanning the entire range of SoCfrom 0 to 1

OCV5 f (SoC) for a hypothesized function f

Some important factors will influence the OCV
SoC curve such asaging and temperature

On the left side ofFig 1.5, the OCV
SoC characterization curves ofnew and aged batteries are shown New battery curves are plotted in solidblue and aged battery curves are plotted in dashed red Different curves ofthe same type correspond to temperatures ranging from 25 to 50 On theright, nominal OCV modeling uses Cnom5 1.5 Ah in computing SoC atall temperatures

There are two main methods for OCV tests: low-current OCV testsand incremental OCV tests;Fig 1.6shown the latter

1.3.1.2 HPPC Test

In order to acquire data to identify the model parameters, a hybrid pulsepower characterization (HPPC) test procedure is conducted at certain SoCintervals (constant current C/3 discharge segments) starting from 1.0 to 0.1and each interval follows by a 2-hour rest to allow the battery to get electro-chemical and thermal equilibrium before applying the next The HPPC cur-rent profile is shown in Fig 1.7 The voltage, current, and SoC profiles ofthe HPPC test are shown inFig 1.7B
D The sampling time is 1 second

Figure 1.5 Aging and temperature will influence the OCV
SoC experiment results Source: Pattipati, B., Balasingam, B., Avvari, G.V., Pattipati, K.R., Bar-Shalom, Y., 2014 Open circuit voltage charaterization of lithium-ion batteries J Power Sources 269, 317
333 (Pattipati et al., 2014).

9

Modeling, Evaluation, and State Estimation for Batteries

1.3.1.3 Driving Cycle Experiment

The dynamic stress test (DST) and the federal urban dynamic schedule(FUDS) test are the commonly used test procedures given in battery testprocedure manuals The DST uses a 360 second sequence of power stepswith seven discrete power levels The DST is a typical driving cycle that isoften used to evaluate various battery models and SoC estimation algo-rithms The SoC profiles and zoomed current profiles of this test are plotted

Figure 1.6 Results of OCV test with certain SoC intervals and rest periods.

Figure 1.7 (A) HPPC current profile; (B) current profiles of the HPPC test; (C) voltage profiles of the HPPC test; (D) calculated SoC profiles of the HPPC test.

inFig 1.8 As the DST driving cycle, the FUDS is a standard time-velocityprofile for urban driving vehicles as well, which can be seen inFig 1.9.

1.3.2 Parameter Identification Methods

1.3.2.1 Offline Methods

To identify the parameters in different models, a least squares (LS) methodand genetic algorithm are presented The LS method can be applied toidentify parameters in different SoCs of the battery via the HPPC testmentioned above Taking the Thevenin model as an example, the state-space equations can be formulated as follows:

_

Up5 IL=Cp2 Up=RpCpSoC5 2 IL=Ca

Ut5 Uoc2 Up2 ILRo

8

>

curve can be fitted by the model:

where z denotes as the SoC The discrete form of this equation can beachieved by using the first-order backward difference:

(1.9)where the coefficients ciare:

where Y is the vector of terminal voltage, Y5 [Ut(1) Ut(2) Ut(N)]T,

To evaluate the accuracy of models, the root mean square error(RMSE) of terminal voltage is set as the indicator Minimizing the index

is the cost function for the optimization problem:

ðUtðiÞ2 ^UtðiÞÞ2

(1.13)where ^Ut is the predicted terminal voltage from the model

1.3.2.2 Online Methods

In order to improve the prediction precision of the battery model, we usethe recursive least squares (RLS) method with an optimal forgetting factor

to carry out online parameter identification

A model-based method can provide a cheap alternative in estimation

or it can be used along with a sensor-based scheme to provide someredundancy The RLS algorithm is based on the minimization of the sum

of squared prediction errors, where estimated process model parametersare improved progressively with each new process data acquired TheRLS method with an optimal forgetting factor (RLSF) has been widelyused in estimation and tracking of time varying parameters in variousfields of engineering Many successful implementations of RLSF-basedadaptive control for time varying parameters estimation are available inthe literature

Consider a single-input single-output (SISO) process described by thegeneral higher-order autoregressive exogenous (ARX) model:

where y is measured system output, which denotes the terminal voltage

Ut in this article ϕ and θ are the information matrix and the unknownparameter matrix, respectively The parameters inθ can either be constant

or subject to infrequent jumps ξ is a stochastic noise variable (randomvariable with normal distribution and zero mean), and k is a nonnegativeinteger, which denotes the sample interval, k5 0, 1, 2,

For the recursive function of Eq (1.13), the system identification isrealized as follows:

KðkÞ5λ 1 ϕPðkTðkÞPðk 2 1ÞϕðkÞ2 1ÞϕðkÞ

PðkÞ5Pðk2 1ÞKðkÞϕλTðkÞPðk 2 1ÞeðkÞ5 yðkÞ 2 ϕðkÞ^θðk 2 1Þ

To achieve an accurate SoC profile to evaluate OCV-based SoC mates, we should build the SoC reference data as “ture” SoC first Due

esti-to the hard determination of the exact SoC value, herein we determinethe initial SoC and the terminal SoC of the lithium iron-phosphate cellaccording to the definition of SoC with a standard charging experiment

13

Modeling, Evaluation, and State Estimation for Batteries

and a further standard discharging experiment after finishing a test, so theinitial SoC and the terminal SoC are accurate The coulomb countingapproach is used to calculate the SoC since it can keep track of the accu-rate SoC with accurate initial SoC, battery capacity and current We alsoimprove the SoC accuracy with a revision method based on the accurateterminal SoC Considering all the battery experiments are carried out in

a temperature chamber the SoC calculation method is feasible with anacceptable accuracy

After setting the initial value P0and θ0, the online parameter cation model coded by Simulink/xPC Target can be used to get themodel’s parameters The online parameter identification results are shown

pro-files,Fig 1.10Bshows the parameter estimation result for the first eter ofθ,Fig 1.10C shows the parameter estimation result for the secondparameter of θ 2 a1, and Fig 1.10D shows the parameter estimationresults for the third and fourth parameter ofθ 2 a2,a3

param-On the one hand, we will evaluate the proposed online parameteridentification performance by the terminal voltage estimation accuracy ofthe dynamic model On the other hand, we will use the online OCV esti-mate to infer battery SoC with the OCV
SoC lookup table

X: 2563 Y: -0.03197

Figure 1.10 The online parameter identification results: (A) terminal voltage; (B) the first parameter of θ; (C) the second parameter of θ; and (D) the third and fourth para- meters of θ.

The maximum error, minimum error, and mean error and RMSE areselected as evaluation indexes to evaluate the estimation accuracy of theterminal voltage observer The estimation error can describe the differ-ence between the experimental data and online estimated value directly.The RMSE is used to evaluate the deviation degree of estimated valueand experiment value, which can describe the present error and the con-vergence of the estimation algorithm together.

accuracy of the terminal voltage, the voltage error between the sensorvalues Fig 1.11A indicates the online parameter identification methodcan estimate the terminal voltage accurately, especially with a bad initialvalue of P0 and θ0 In addition, the proposed method has robust perfor-mance for a bad initial value Fig 1.11A gives a direct reflection of theconvergence characteristics for the proposed online parameters identifica-tion method, and the terminal voltage estimation result based on theRLSF algorithm with convergence to the true value within less than 30sample intervals (the sample interval is 1 second) The detail error index

is shown in Table 1.1 Although the absolute error is 1.2292 V, it

–1.5 –1 –0.5 0 0.5

converges to the true value quickly, so both the error and the RMSE(nominal voltage is 32 V of the battery module) are less than 1%.

The online estimation results for the OCV and the ohmic resistancecan be deduced fromFig 1.10, and are shown in Fig 1.12 We can cal-

SoC
OCV data The comparative profiles between true SoC and mated SoC are shown inFig 1.13A, and the SoC estimated error profiles

shows that the OCV values provide an acceptable way to estimate the

Table 1.1 Statistic list of model errors

battery SoC with good robustness regardless of the initial value; its SoCestimate error is shown in Fig 1.13B, which shows the fluctuation of itserror is within 0.04 after several sampling times when the online parame-ter identification process is stable Its RMSE performance shows that theSoC estimation error is getting smaller and converging to zero quickly.Therefore the online parameter identification method not only canensure the dynamic voltage simulation accuracy of the Thevenin modelwith real-time model parameters, but also can provide an acceptable SoCestimation and a maximum error within 4%.

1.3.3 Evaluation of n-RC Networks Model

For Li-ion batteries, based on an analysis on the structure of the Rintmodel and the Thevenin model, an equivalent circuit model with n-RCnetworks, named the NP model hereafter, is built Fig 1.14 shows the

NP model where IL is the load current with a positive value in the charge process and a negative value in the charge process, ULis the termi-nal voltage, Uoc is the OCV, Ro is the equivalent ohmic resistance, Ci isthe ith equivalent polarization capacitance, Riis the ith equivalent polari-zation resistance simulating the transient response during a charge or

0.4 0.6 0.8 1

SoC error RMSE Lower bound Upper bound (B)

(A)

X: 4117 Y: 0.04

X: 4117 Y: –0.04

Figure 1.13 OCV estimates based on SoC estimation accuracy: (A) SoC estimation results and (B) RMSE performance.

17

Modeling, Evaluation, and State Estimation for Batteries

discharge process, and Ui is the voltage across Ci i5 1, 2, 3, 4, , n.The electrical behavior of the NP model can be expressed byEq (1.15)

in the frequency domain:

The NP model is simplified as the Rint model and a discretization form

step with a sample interval of T, k5 1, 2, 3, :

–

_

Figure 1.14 Schematic diagram of the NP model.

follow-ing assumptions: The@SoC=@t  0 holds for small battery energy is sumed or regained relative to totally useable capacity; relying on theproper design of a cooling system/heater of BMS, the temperature

con-19

Modeling, Evaluation, and State Estimation for Batteries

increase/decrease of batteries should be slow, the@Tem=@t  0 holds fornormal operating conditions; and the@H=@t  0 definitely holds since Hrepresents a long usage history.

Gðz21Þ 5b31 b4z211 b5z22

where b1, b2, b3, b4, and b5 are the coefficients solved from Eq (1.32).Similar to the case of n5 1, a discretization form ofEq (1.31)is arranged

as Eq (1.34), where k5 2, 3, 4, :

ULðkÞ 5 ð1 2 b12 b2ÞUocðkÞ 1 b1ULðk 2 1Þ 1 b2ULðk 2 2Þ

1 b3ILðkÞ 1 b4ILðk 2 1Þ 1 b5ILðk 2 2Þ (1.34)Define

ϕ2ðkÞ 5 1 U Lðk 2 1Þ ULðk 2 2Þ ILðkÞ ILðk 2 1Þ ILðk 2 2Þ ,

yk5 ULðkÞ, and θ2ðkÞ 5 ð12b 12b2ÞUoc b1 b2 b3 b4 b5T

,then

toEq (1.29) andEq (1.34), where k5 n, n 1 1, n 1 2, :

21

Modeling, Evaluation, and State Estimation for Batteries

(1.38)Similarly, a recursive function is built as Eq (1.39)with the input vec-torϕnðkÞ, parameters vector θnðkÞ, and the output yk5 ULðkÞ:

is used such as Kalman filters, huge computing costs will result due to thecomplex model structure Thus the evaluation tests are only conductedfor the General equivalent circuit model (GECM) models with n5 1
5and the results are shown inFig 1.18

test, the maximum of the absolute voltage error is within 32 mV and themaximum of the RMSE is less than 15 mV.Fig 1.18Ashows that for theHPPC test, the GECM model with one RC network has the biggestvoltage error while the GECM model with two RC networks performsbest, but the mean of voltage error is not significant when comparedwith the GECM model with three, four, or five RC networks

Model structure number

Shepherd model

Nernst model

(D) (C)

Local enlarge

Figure 1.15 Evaluation results under the HPPC test: (A) the statistics results of the age error; (B) the statistics results of the RMSE; (C) the voltage profiles of the Shepherd model-based estimation, the Nernst model-based estimation, and the HPPC test; and (D) the voltage profiles of the DP model-based estimation and the HPPC test.

–100 –50 0 50

Model structure number

Model structure number

Fig 1.18Bshows that the statistics of the RMSE are less than 1 mV, and

that the GECM model with two RC networks has the smallest statisticvalues among the five models for the DST test; Fig 1.18D shows theGECM model with two RC networks has the smallest mean of the RMSEwhile its maximum of the RMSE is bigger than the GECM model withfive RC networks However, the GECM model with two RC networks issimpler than that with five RC networks and is still the nest battery modelafter considering the practical applications.Fig 1.18E and F show that forthe FUDS test, the maximum of the voltage error of the GECM modelwith five RC networks performs better than the GECM model with two

RC networks, but the GECM model with two RC networks performs thebest in the absolute minimum, the mean of the voltage errors, and statisticsvalues of the RMSE It can be concluded that the GECM model with two

RC networks still shows the best performance

In summary, the GECM model with two RC networks, also called the

DP model, is the best model for the Li-ion battery simulation Further, itdoes not mean that the more RC networks the model has, the more accu-rate the model is On the contrary, the performance of the GECM modelwith more than three RC networks becomes worse in some aspects

Model structure number

6 8 10 12 14 16

Model structure number

1.4 STATE ESTIMATION

1.4.1 Definition of SoC

The SoC is a relative quantity that describes the ratio of the remainingcapacity to the present maximum available capacity of a battery, and it isgiven by

SoCt5 SoC02

ðt0

where SoCt is the present SoC, SoC0 is the SoC initial value, IL,t is theinstantaneous load current (assumed positive for discharge, negative forcharge),η is the Coulomb efficiency, which is the function of the current

With two RC networks

With two RC networks

With five RC networks

With two RC networks

With five RC networks

With two RC networks

Figure 1.18 Evaluation results of the GECM models: (A) the statistics results of the voltage error under the HPPC test; (B) the statistics results of the RMSE under the HPPC test; (C) the statistics results of the voltage error under the DST test; (D) the statistics results of the RMSE under the DST test; (E) the statistics results of the volt- age error under the FUDS test; and (F) the statistics results of the RMSE under the FUDS test.

25

Modeling, Evaluation, and State Estimation for Batteries

and the temperature; and Ca is the present maximum available capacity,which may be different from the rated capacity for the age effect.

DescribingEq (1.42)with a discrete-time form

1.4.2 Classification of Estimation Methods

A wide variety of SoC estimation methods have been put forward toimprove battery SoC determination (Thackeray et al., 2012; Cuma andKoroglu, 2015; Fleischer et al., 2014; Wang et al., 2015; Dubarry et al.,2007; Einhorn et al., 2012; Waag and Sauer, 2013; Cuadras and Kanoun,2009; KongSoon et al., 2009; Yang et al., 2015; Plett, 2004b, 2006;

each with its advantages Table 1.2 illustrates a systematic classificationand comparison mainly for existing SoC estimation methods Thesemethods can be roughly divided into four groups; namely look-uptable methods, ampere-hour methods, model-based methods, and data-driven methods

Look-up table methods are simple but not suitable for online tion and require regular recalibration for battery OCV, electrochemicalimpedance spectroscopy (EIS), etc (Dubarry et al., 2007; Einhorn et al.,

The ampere-hour methods are widely employed because they canachieve the online estimation of SoC with low computational cost expe-

suitable sampling period, and precision, the methods can obtain accurateestimation of SoC at a certain time or interval But for the actual operat-ing conditions of an EV, it is impossible to achieve Thus the open-loopmethods are greatly affected by a small disruption, such as the change ofworking temperature (KongSoon et al., 2009; Yang et al., 2015) and need

to be used in combination with other algorithms for constant correction.Model-based methods can overcome the drawbacks associated withthe above-mentioned two methods and provide the robust performance

Table 1.2 Comparison of SoC estimation techniques ( Lin et al., 2016 )

Methods Advantages Disadvantages Accuracy Robustness

• Low calculation cost

• Satisfactory real-time performance.

• Susceptible to uncertain factors, such as

temperature, aging, and driving cycles;

• Requires regular calibration for battery OCV, EIS, etc.;

• Requires expensive test equipment.

• Low calculation cost;

• Excellent time

real-performance.

• Requires an accurate initial value;

• Uses open-loop calculation and lacks the necessary correction;

• Susceptible to unavoidable current drift, noisy disturbance and aging.

• Good real-time performance.

• Strong adaptability.

• Requires a field battery model;

high-• High calculation cost;

• Tremendous discrepancy in their robustness and reliability.

• High computational complexity;

• Highly dependent on the training data.

Excellent Poor

27

Modeling, Evaluation, and State Estimation for Batteries

needed for SoC estimation due to the closed-loop feedback mechanism

presented an equivalent circuit model-based SoC estimation methodusing an extended Kalman filter (EKF), which makes the traditionalKalman filter appropriate for a nonlinear system Plett (2006)presented acomparative study of the equivalent circuit model-based SoC estimationalgorithms using EKF and sigma point Kalman filtering (SPKF), evaluatedwith the estimated value and error bound The results showed that theSPKF was better than the EKF.Xiong et al (2013) proposed a novel SoCestimation method for a battery pack based on an adaptive extendedKalman filter (AEKF) The results showed that these kinds of model-based methods have good robustness and accuracy (Hu and Yurkovich,2012; Zhang et al., 2008, 2012; Xu et al., 2014; Xia et al., 2014; Chen

et al., 2014)

2015), support vector regression (SVR) (Anton et al., 2013; Sheng and

estima-tion of SoC based on an adaptive wavelet neural network Dai et al

SoC correction.Sheng and Xiao (2015) proposed a kind of SoC tion method based on a fuzzy least squares support vector machine,which can reduce the effects of the samples with low confidence.Generally speaking, these methods have their respective advantages ofaddressing the problem of nonlinearity but require large amounts ofexperimental data to train the model If the data cannot reflect the com-prehensive features of the battery, the SoC estimation error can be verylarge

estima-1.4.3 Description of AEKF Algorithm

This section mainly describes the AEKF algorithm and its application inthe BMS

1.4.3.1 AEKF Approaches

The Kalman filter is a mathematical technique that provides an efficientrecursive means for estimating the states of a process in such a way as tominimize the mean of the squared error The filter has been appliedextensively in the field of state estimation, parameter estimation, and

continuous-time dynamics with discrete time measurements given by

A drawback of the Kalman filter is its dependence on a good estimation

of Q and R A Kalman filter basically assumes that the covariances of boththe process and the measurement noise are known Thus, in practice, inap-propriate initial noise information will make the approach fail to ensure itsperformance Otherwise, the covariance values can be estimated to improvethe performance of the Kalman filter by employing an adaptive Kalman fil-ter Mehra classified adaptive Kalman filter methods into four categories:(1) Bayesian, (2) maximum likelihood, (3) correlation, and (4) covariancematching These adaptive Kalman filter methods have been applied toother applications, including an inertial navigation system and a global posi-tioning system In this section, an AEKF employing the covariance-matching approach was applied to realize a robust SoC estimation

The AEKF provides further innovation in the algorithm using the ter’s innovation sequence The innovation allows the parameters Qk and

fil-Rk to be estimated and updated iteratively from the following equations(Schmidt et al., 2010):