sensors Article

A Method to Simultaneously Detect the Current Sensor Fault and Estimate the State of Energy for Batteries in Electric Vehicles Jun Xu 1,2, *, Jing Wang 1,2 , Shiying Li 1,2 and Binggang Cao 1,2 1 2

*

School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China; [email protected] (J.W.); [email protected] (S.L.); [email protected] (B.C.) State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China Correspondence: [email protected]; Tel.: +86-29-8266-8835

Academic Editor: Vittorio M. N. Passaro Received: 25 May 2016; Accepted: 16 August 2016; Published: 19 August 2016

Abstract: Recently, State of energy (SOE) has become one of the most fundamental parameters for battery management systems in electric vehicles. However, current information is critical in SOE estimation and current sensor is usually utilized to obtain the latest current information. However, if the current sensor fails, the SOE estimation may be confronted with large error. Therefore, this paper attempts to make the following contributions: Current sensor fault detection and SOE estimation method is realized simultaneously. Through using the proportional integral observer (PIO) based method, the current sensor fault could be accurately estimated. By taking advantage of the accurate estimated current sensor fault, the influence caused by the current sensor fault can be eliminated and compensated. As a result, the results of the SOE estimation will be influenced little by the fault. In addition, the simulation and experimental workbench is established to verify the proposed method. The results indicate that the current sensor fault can be estimated accurately. Simultaneously, the SOE can also be estimated accurately and the estimation error is influenced little by the fault. The maximum SOE estimation error is less than 2%, even though the large current error caused by the current sensor fault still exists. Keywords: fault detection; state of energy estimation; battery model; proportional integral observer; battery management systems; electric vehicle

1. Introduction Due to pollution and the energy crisis, electric vehicles (EVs), including battery electric vehicles (BEVs), hybrid electric vehicles (HEVs) and plug-in hybrid electric vehicles (PHEVs) are of great importance [1–3]. In order to cope with the power and energy demands for such applications, a stable lithium-ion battery pack should be constructed with a large number of battery cells connected in series or parallel. A battery management system (BMS) is utilized to maintain optimum battery performance and ensure safety in EVs. As the key functions of the BMS, the State of Charge (SOC), the State of Health (SOH) and State of Energy (SOE) should be monitored online. As for the application of EVs, how much the remaining driving range of EVs left is a critical point that people should focus on. In fact, the SOE, which signifies the residual available energy in the battery, is more qualified than SOC to estimate the remaining driving range [4,5]. Unfortunately, SOE cannot be measured directly. As the most important information source for the SOE estimation, current sensor may fault, and the current information provided may have a bias. Consequently, accurate SOE estimation for batteries remains quite challenging and problematic. An assortment of techniques has previously been reported to estimate the SOC of the batteries in EVs, each having its relative merits. The ampere-hour counting/integral (coulomb counting) Sensors 2016, 16, 1328; doi:10.3390/s16081328

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method (ACM) is based on current measurement and integration, which is considered as the most common SOC estimation method. However, the prior knowledge of initial SOC is needed and it suffers from accumulated errors of noise and measurement error [6,7]. Although open-circuit voltage (OCV) method is very accurate, it needs a long rest time to estimate the SOC and thus it cannot be used in real time applications [6]. Besides, the sliding mode observer based estimations [8–11], the extended Kalman filtering (EKF) based estimators [12–15], the proportional integral observer (PIO) based estimations [16–19], the support vector based estimators [20], the neural networks (NNs) [21,22] and the fuzzy logic principle based estimations [23], etc. have been widely applied to estimate the SOC of batteries. With respect to the SOE estimation, some studies have been conducted. The Back-Propagation Neural Network (BPNN) based method was utilized in [24] to estimate the SOE. The method considered the influence of the energy loss on the internal resistance, the electrochemical reactions, the decline of OCV, the discharge rate and the temperature fluctuation. However, the method is too complex to be widely implemented in practical applications. H. He et al. [25] chose the central difference Kalman filter (CDKF) and Gaussian model to estimate the SOE and concluded that the estimation error was small. Wang et al. [26] proposed a joint estimation approach based on PF algorithm to obtain the SOC and SOE respectively. However, the estimation accuracy of SOE relies on the prerequisite that the SOC has been well computed. Dong et al. [27] adopted dual filters-EKF plus PF-to estimate the SOE. The former filter is employed to update parameters of battery model on-line while the other filter is used to estimate the SOE. The recursive least square (RLS) with forgetting factor method was applied to identify the battery model and adaptive technique to estimate the SOE [28]. The simulation results demonstrated the effectiveness of the method. Barai et al. [4] presented a novel SOE estimation method based on the short-term cycling history. Till now, the aforementioned methods have been studied and acceptable achievements have been made in different applications. However, most of the methods stated above were relied on the current information, namely the current sensor. What if the current sensor fails? Without proper actions, the estimated SOE will be useless, which may be dangerous for the batteries as over-charge or over-discharge may occur. Actually, the application of fault detection and diagnosis is not new, extensive work in this area has been conducted with focus on different faults and related techniques. Permanent magnet demagnetization for IPMSMs was detected with nonsingular fast terminal-sliding-mode observer in [29]. Gang Huang et al. took advantage of sliding mode observer to detect the fault of the current sensor for PMSM drive systems [30]. In addition, fault detection is also becoming more and more important with efforts concentrated on detecting different battery faults. A. Izadian et al. proposed a special type of observer based fault detection technique, namely the multiple model adaptive estimation technique, and the performance shift in lithium ion batteries since over discharge could be detected [31,32]. Synthesized design of Luenberger observer (LO) was adopted in [33], along with equivalent circuit model (ECM) for fault isolation and estimation. The LO is a suitable candidate for fault detection in systems with little or no measurement noise. However, with the presence of noise, this setup has been confronted with inherent difficulties, particularly with performance variations. An adaptive model based technique was used to diagnose the over-charge and over-discharge faults in Li-ion batteries [34]. The authors adopted a conditional three-parameter capacity degradation model in [35]. Battery parameter identification, estimation and prognosis methodology were presented using several techniques, e.g., neural network (NN), auto regressive moving average (ARMA), fuzzy logic (FL) and impedance spectroscopy (IS), etc. [36]. With the support of these methods, the stated faults can be detected before the faults can go to extreme conditions. However, it is obvious that the related faults stated above are mostly about battery itself, but few is about sensor, especially about the current sensor used for SOE estimation. Satadru Dey et al. took advantage of three sliding mode observer to estimate three sensor faults independently [37]. Zhentong Liu et al. realized the detection and isolation of five faults, including the

the current sensor fault [38]. However, most studies are satisfied when the faults are detected. How to fix the fault or how to take measures to reduce the influence of the faults still remains to be solved. In this work, the proportional integral observer (PIO) is introduced to simultaneously detect the current sensor fault and estimate the SOE. By taking advantage of the unique properties of the PIO, Sensors 2016, 16, 1328 3 of 15 the current fault could be isolated from the state estimation, and thus, accurate current sensor fault could be obtained. Besides, with the accurate estimated results, the fault influence could be effectively current sensor fault [38]. However, most studies are satisfied when the faults are detected. How to fix eliminated. As a result, the SOE estimation could be accurate and robust, even the current sensor the fault or how to take measures to reduce the influence of the faults still remains to be solved. fault has occurred. Thethe remainder ofintegral this paper is organized as follows: In Sectiondetect 2, thethe simplified In this work, proportional observer (PIO) is introduced to simultaneously battery model is introduced thethe state space expression of of thethebattery is deduced. current sensor fault and and estimate SOE. By taking advantage unique model properties of the PIO, The PIO the current fault could be isolated from the state estimation, and thus, accurate current sensor based current sensor fault detection and SOE estimation method are proposed and fault analyzed in could be obtained. Besides, with the accurate estimated results, the fault influence could be effectively Section 3; Section 4 establishes simulations and experiments validation and the results are analyzed. eliminated. As a result, the SOE estimation could be accurate and robust, even the current sensor fault Conclusions are provided in Section 5. 2.

has occurred. The remainder of this paper is organized as follows: In Section 2, the simplified battery model is introduced and the state space expression of the battery model is deduced. The PIO based Battery Model Building and Analysis current sensor fault detection and SOE estimation method are proposed and analyzed in Section 3; Section 4 establishes simulations and experiments validation and the results are analyzed. Conclusions In order to achieve a reliable battery state estimation and fault detection, an accurate model must are provided in Section 5.

be built first. Taking accuracy and computation complexity into consideration, the simplified battery Battery Model and Analysis model is2. introduced toBuilding characterize the battery. The schematic diagram for the simplified battery model is shown in to Figure 1.aAs shown in the several commonly electric components are In order achieve reliable battery statefigure, estimation and fault detection,used an accurate model must built first. is Taking accuracy and computation complexity intoseries consideration, the simplified battery utilized.beThe OCV adopted to describe the voltage source; resistance ( R1 ) is used to describe model is introduced to characterize the battery. The schematic diagram for the simplified battery

the electrical resistance of various battery components; the diffusion resistance ( R2 ) and the diffusion model is shown in Figure 1. As shown in the figure, several commonly used electric components are

utilized. OCV is adopted the voltage source; series resistance to describe capacitance ( C2The ) consisting of a to RCdescribe network are adopted to describe the(Rmass transport effects and 1 ) is used electricalperformances; resistance of various components; theassumed diffusion resistance the diffusion 2 ) and positive(Rfor charge while negative dynamicthevoltage the battery load current I is capacitance (C2 ) consisting of a RC network are adopted to describe the mass transport effects and Vo and V1 is thetheterminal voltage and the voltage over R respectively, V2 for discharge; dynamic voltage performances; load current I is assumed positive for charge while1 negative for

( z ) in this discharge; Vo and V and the voltage over R1OCV respectively, V2 describes describes the diffusion voltage over thevoltage RC network. The battery is denoted as Vocthe 1 is the terminal diffusion voltage over the RC network. The battery OCV is denoted as V ( z ) in this model to describe oc for battery SOE. model to describe the OCV under different SOEs, where z is the abbreviation the OCV under different SOEs, where z is the abbreviation for battery SOE. V2

V1

R2 R1 Voc =f(z)

+

C2

Voc(z)

Vo I

-

Figure 1. The simplified battery model.

Figure 1. The simplified battery model. According to the circuit theory, Equations (1) and (2) could be obtained to describe the electrical

According to of the theory, Equations (1) and (2) could be obtained to describe the electrical relationship thecircuit different parameters in the model. relationship of the different parameters in the model. .

V2 = −

1 1 V2 + I R2 C12 C2 1

V2  

V2 

Vo = Voc (Rz2)C +2V1 + VC 2 2

(1)

I (2)

According to the definition of SOE, which is the ratio of the remaining energy to the nominal Voc ( z as ) Equation V1  V2 (3). energy, the mathematical relationship canVbe written o 

(1)

(2)

Zt of the remaining energy to the nominal According to the definition of SOE, which is the ratio 1 z(t) = z(0) + ∆z = z(0) + P(τ )dτ (3) energy, the mathematical relationship can be written as EEquation (3). n 0

t

1 z (t )  z (0)  z  z (0)  P ( ) d En 0

(3)

where z (0) and z (t ) are abbreviations of the initial SOE and the SOE at time t respectively; z is the variation of battery SOE during the time period from 0 to t, P( ) is the instantaneous battery

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where z(0) and z(t) are abbreviations of the initial SOE and the SOE at time t respectively; ∆z is the variation of battery SOE during the time period from 0 to t, P(τ ) is the instantaneous battery power, and En is the nominal battery energy. Since z(0) is a constant for any given situation, Equation (3) can be rewritten as: . 1 z= P (4) En If V2 and z are chosen as the states of the battery model, the state function can be written as: .

(

V 2 = − R21C2 V2 + C12 I . z = E1n P = EVno I

(5)

For a given nonlinear system, the relationship between SOE and Voc (z) can be divided into several sections, and the subsystem in each section is considered to be linear [39]. Thus, the relationship can be written in the short SOE interval as follows for the ith SOE interval (i − 1) · ∆SOE ≤ SOEi ≤ i · ∆SOE : Voc = ai · SOEi + bi

(6)

where ∆SOE is the SOE interval length. According to the explanation above, the output Equation can be described as: Vo = Voc + V1 + V2 = ai · z + bi + R1 · I + V2

(7)

The state space function with the additional state z can be rewritten as: (

" where A =

− R21C2 0

0 0

#

" ,B=

1 C2 Vo En

.

x = Ax + Bu y = Cx + Du

# ,C=

h

1

ai

i

(8) "

, D = R1 , x =

V2 z

# , y = Vo − bi , u = I.

3. The Method to Simultaneously Detect the Current Sensor Fault and Estimate the SOE Based on Proportional Integral Observer In this section, the current sensor fault is assumed to be a delta value between the actual current and the measured current. Such delta current fault is denoted as current sensor fault f . Given that the battery model is affected by the current sensor fault, the state space Equation is given as follows: (

.

x = Ax + B(u + f ) y = Cx + D (u + f )

(9)

where x ∈ R2×1 represents the battery states, which is V2 and z as stated in previous section, y ∈ R1×1 is the measured output, u ∈ R1×1 is the system’s input, which is the current I in the battery model, f represents the current sensor fault. A, B, C and D are known coefficients matrices with appropriate dimensions, which could be identified from the test data of batteries. In order to take advantage of the unique properties of the PIO, the PIO is applied to the battery model and the observer is designed as follows:  .  x + Bu + K p (y − ye) + Ki2 fe   xe = Ae .

fe = Ki1 (y − ye)    ye = Ce x + Du

(10)

 y  Cx  Du 

Note that variable f is defined as the integral of the difference ( y  y ) , which represents the Sensors 2016, 16, 1328

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K p   21 is the proportional gain, Ki1 11 and

estimated current sensor fault. Vectors

Noteintegral that variable fe is The defined as the block integralof of the the difference (y −current ye), whichsensor represents Ki 2   21 are the gains. design PIO based fault detection the estimated current sensor fault. Vectors K p ∈ R2×1 is the proportional gain, K

∈ R1×1 and

i1 and compensation is shown in Figure 2. K ∈ R2×1 are the integral gains. The design block of the PIO based current sensor fault detection i2

and compensation is shown in Figure 2.

Reference SOE

Measured Voltage Current Battery Current Sensor

PIO + + B

. x~

+

Kkp ~

Ki2

1 C S

+

f

1 C S

x~

. ~ f

C

SOE Error Ki1

+

A

Estimated SOE

D ~

Measured Current Reference Current

Estimated Current Sensor Fault f

Fault Error Reference Current Sensor Fault f

Figure 2. The method to simultaneously detect the current sensor fault and estimate the SOE.

Figure 2. The method to simultaneously detect the current sensor fault and estimate the SOE. It is supposed that the fault affecting the system is bounded. The expressions of the state reconstruction the fault reconstruction are provided by the Equations as follows: supposed thaterror theandfault affecting the error system is bounded. The expressions

It is of the state ( reconstruction error and the fault reconstruction error ex = x − xeare provided by the Equations as follows: (11)

e f = f − fe

ex  x  x . The dynamics of the state reconstruction  error is given by the computation of ex which can be written as: e f  f  f . . . e x = x − xe = (A − K p C)ex + B f − Ki2 fe − K p D f

(12)

e x = x − xe = (A − K p C)ex + Be f − K p D f

(13)

(11)

ex bewhich can be The dynamics of the the state reconstruction is given byB,the To estimate current sensor fault, it iserror designed that Ki2 = thus,computation the Equation (12)of could written as: rewritten as follows: . . .

ex  x is xgiven  (A K p C)ex  Bf  Ki 2 f  K p Df The fault error estimation as follows: .

.

.

. fe = f − Ki1 Cex − Ki1 D fK e f = fit−is fault, designed that

To estimate the current sensor be rewritten as follows: The following matrices are introduced:

i2

(12)

(14)  B , thus, the Equation (12) could

 ex e  Be  K Df  ex  x  x  (A  K C)  x f p  ϕ= p 

"

ef



The fault error estimation is given as

  follows:    ε=

#

"

f

#

(15)

.

f

 e f  f  f  f  Ki1Cex  Ki1 Df The following matrices are introduced:

(13)

(14)

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From the Equations (13)–(15), the following Equation can be obtained: .

ϕ = Ae ϕ + Be ε with:

" Ae = " Be =

A − KpC −Ki1 C

−K p D −Ki1 D

B 0 # 0 I

(16) # (17)

(18)

where the matrix I is the identity matrix with appropriate dimensions. The convergence of error Equation can be proved by choosing the Lyapunov candidate function as follows: V = ϕ T Pϕ

(19)

where P indicates a defined positive matrix. The state reconstruction error ex and the fault . reconstruction error e f tend towards zero if V < 0 according to the Lyapunov theory. .

.T

.

V = ϕ Pϕ + ϕ T P ϕ = ( ϕ T AeT + ε T BeT ) Pϕ + ϕ T P( Ae ϕ + Be ε)

= ϕ T AeT Pϕ + ε T BeT Pϕ + ϕ T PAe ϕ + ϕ T PBe ε It could be rewritten as: "

#

"

.

V = ψ T Πψ #

(20)

(21)

ϕ AeT P + PAe PBe ,Π= . ε BeT P 0 The resolution of the inequality Π < 0 leads to the values of K p and Ki1 . By these procedures, the differential of the Lyapunov candidate function is assured to be negative, which means when t → ∞ , estimated state xe would converge to true state x and the estimated fault fe will converge to the true fault f .

where ψ =

4. Simulation and Experimental Validation To verify the effectiveness of the proposed strategy for current sensor fault detection and compensation, the simulation and experimental validation are established. The experiment data used for this study are acquired through the battery test bench set up as shown in Figure 3, which consists of a battery cycler, a temperature chamber for environment control, a computer with dSPACE for performing the proposed method and experimental data storage. As shown in the figure, the battery cycler, which is controlled by the computer with TCP/IP, is used to apply current profile to the battery. Meanwhile, the voltage, current and temperature are measured by the battery cycler and the data will be sent to the computer. It is assumed in the paper that the message measured by the battery cycler is relatively true, and the stored data will act as the reference signals. For example, the current will be applied to calculate the SOE and the reference SOE could be obtained. The battery is placed in a temperature chamber to simulate the temperature environment of the battery when in practical implementation. The dSPACE DS1104 control board is utilized in this paper to perform the proposed algorithm. The current signal is measured by the current sensor through an ADC, and the voltage of the battery is measured directly through another ADC of the control board. The proposed algorithm is conducted with the Matlab/Simulink environment. After the algorithm is validated with the simulation in the Matlab/Simulink environment, the model will be modified and downloaded to the dSPACE control board. The dSPACE control board performs the algorithm and sends the calculated data back to the computer, such as the estimated SOE, estimated current sensor fault etc. The nominal capacity of the tested battery is 20 Ah, with 3.7 V nominal voltage.

ADC of the control board. The proposed algorithm is conducted with the Matlab/Simulink environment. After the algorithm is validated with the simulation in the Matlab/Simulink environment. After the algorithm is validated with the simulation in the Matlab/Simulink environment, the model will be modified and downloaded to the dSPACE control board. The environment, the model will be modified and downloaded to the dSPACE control board. The dSPACE control board performs the algorithm and sends the calculated data back to the computer, dSPACE control board performs the algorithm and sends the calculated data back to the computer, such as the estimated SOE, estimated current sensor fault etc. The nominal capacity of the tested such as the16,estimated SOE, estimated current sensor fault etc. The nominal capacity of the tested Sensors 2016, 1328with 3.7 7 of 15 battery is 20 Ah, V nominal voltage. The upper cut-off voltage and the lower cut-off voltage battery is 20 Ah, with 3.7 V nominal voltage. The upper cut-off voltage and the lower cut-off voltage are 4.2 V and 2.75 V, respectively. Based on the tested data, the least square method is introduced to are 4.2 V and 2.75 V, respectively. Based on the tested data, the least square method is introduced to R1 , R2areand C2and calculate parameters the battery . The calculated parameters The upperthe cut-off voltage of and the lower model cut-off voltage 4.2 V 2.75 V, respectively. Basedfor on the the R1 , R2 and C2 . The calculate the parameters of the battery model calculated parameters for the battery model are: R1 =square 0.0027method Ω, R2 = 0.0042 Ω, C2 = 25000 F, ai = [0.0032, 0.0071, 0.0052, 0.0051, 0.0029, tested data, the least is introduced to calculate the parameters of the battery model battery model are: R1 = 0.0027 Ω, R2 = 0.0042 Ω, C2 = 25000 F, ai = [0.0032, 0.0071, 0.0052, 0.0051, 0.0029, R1 , R2 and C2 . 0.0085, The calculated parameters the battery R1 = 0.0027 Ω, R2 = 0.0042 Ω, 0.0033, 0.0051, 0.0079, 0.0088, 0.0100,for 0.0111, 0.0111]model and bare: i = [3.5264, 3.5071, 3.5252, 3.5286, b = [3.5264, 0.0033, 0.0051, 0.0085, 0.0079, 0.0088, 0.0100, 0.0111, 0.0111] and C = 25000 F, a = [0.0032, 0.0071, 0.0052, 0.0051, 0.0029, 0.0033, 0.0051, 0.0085, 3.5071, 0.0079, 3.5252, 0.0088, 3.5286, 0.0100, 2 i i 3.5952, 3.5772, 3.4892, 3.281, 3.3244, 3.25, 3.1447, 3.044, 3.044], respectively. The relationship between 0.0111, 0.0111] and b = [3.5264, 3.5071, 3.5252, 3.5286, 3.5952, 3.5772, 3.4892, 3.281, 3.3244, 3.25, 3.1447, 3.5952, 3.5772, 3.4892, i 3.281, 3.3244, 3.25, 3.1447, 3.044, 3.044], respectively. The relationship between OCV and SOE is shown as Figure 4. 3.044, 3.044], respectively. relationship between OCV and SOE is shown as Figure 4. OCV and SOE is shown asThe Figure 4.

Figure 3. Experimental battery test work bench. Figure 3. 3. Experimental battery test test work work bench. bench. Figure Experimental battery

OCV (V) OCV (V)

4.2 4.2 4 4 3.8 3.8 3.6 3.6 3.4 3.4 0 0

20 20

40 60 40SOE (%) 60 SOE (%)

80 80

100 100

Figure 4. The relationship between OCV and SOE. Figure 4. The relationship between OCV and SOE. Figure 4. The relationship between OCV and SOE.

The urban urban dynamometer driving schedule schedule (UDDS) (UDDS) is is an an automobile standard vehicle The dynamometer driving automobile industry industry standard vehicle The urban dynamometer driving schedule (UDDS) is for an automobile industry standard vehicle vehicle time velocity profile for urban driving that has been used a number of years for time velocity profile for urban driving that has been used for a number of years for electric electric vehicle time velocity profile for urban driving that has been used for a number of years for electric vehicle performance testing. testing. The The current current profile profile computed computed from from the the UDDS UDDS and and scaled scaled to to percent percent of of peak peak performance performance testing. The current profile computed from the UDDS andbattery scaledwhen to percent of peak discharge power is utilized to emulate the real power requirement for the it is equipped discharge power is utilized to emulate the real power requirement for the battery when it is equipped discharge powerstudy, is utilized to emulate thecurrent real power requirement for(90 theA). battery when it is equipped in an thethe peak discharge waswas set to rate The SOE profile in an EV. EV.InInthis this study, peak discharge current set4.5toC4.5 C rate (90 A).reference The reference SOE in an EV. In this study, the peak discharge current was set to 4.5 C rate (90 A). The reference SOE is calculated using definition methodmethod with thewith measured data. data. profile is calculated using definition the measured profile is calculated using definition method with the measured data. 4.1. Simulation Study for the Proposed Method In order to demonstrate the effectiveness of the proposed method, based on the above experimental results, the parameters of the battery model are calculated. The battery model is used to calculate the voltage response of the battery. Meanwhile, the same battery model parameters are also adopted in the proposed current sensor detection and SOE estimation method. The parameters for the method are: Kp = [0.5; 0.5], Ki1 = [85], Ki2 = [8e − 5; 1.389e − 3], respectively.

4.1. Simulation Study for the Proposed Method In order to demonstrate the effectiveness of the proposed method, based on the above experimental results, the parameters of the battery model are calculated. The battery model is used to calculate the voltage response of the battery. Meanwhile, the same battery model parameters are Sensors 2016, 16, 1328 8 of 15 also adopted in the proposed current sensor detection and SOE estimation method. The parameters for the method are: Kp = [0.5; 0.5], Ki1 = [85], Ki2 = [8e − 5; 1.389e − 3], respectively. Firstly, to works well is Firstly, to verify verify the theproposed proposedmethod, method,the thenormal normalsituation situationwhen whenthe thecurrent currentsensor sensor works well firstly studied, as shown in Figure 5. In this situation, the battery is charged to full, which means that is firstly studied, as shown in Figure 5. In this situation, the battery is charged to full, which means the initial SOE SOE of theofbattery is 100%. Figure 5a,b are resultsresults of theof estimated SOE ofSOE the that the initial the battery is 100%. Figure 5a,bthe aresimulation the simulation the estimated proposed method, and theand comparison betweenbetween the estimated voltage and the measured voltage is of the proposed method, the comparison the estimated voltage and the measured shown in SOE showresults that the estimated SOE converges to converges the reference voltage isFigure shown5c. in The Figure 5c.estimation The SOE results estimation show that the estimated SOE to SOE,reference which has been proved the previous section for the properties of the the properties PIO. In addition, SOE the SOE, which hasinbeen proved in the previous section for of the the PIO. In estimationthe error also give samealso conclusion. with the zoom figure thezoom SOE addition, SOEresults estimation errorthe results give the Besides, same conclusion. Besides, withofthe estimation error it is obvious that the the reference figure of the SOEresults, estimation error results, it estimated is obviousSOE thattraces the estimated SOE trajectory traces theaccurately, reference with less than 0.01% SOE error. SOE The main reasonerror. is thatThe themain battery model is very trajectory accurately, withestimation less than 0.01% estimation reason is that theaccurate battery in this simulation. The voltage estimation results show that the voltage prediction error is less than model is very accurate in this simulation. The voltage estimation results show that the voltage 10 mV, which is very prediction error is lessaccurate. than 10 mV, which is very accurate. (b)

(a) 100

SOE (%)

SOE (%)

60

69

40

68

20

66 2450

1000

2500

2550

2000

2600

3000 T ime (s)

4

5000

6000

3.8 3.85 3.8 3.75 2500

0

1000

-0.02

0

2000

2540

3000 T ime (s)

2000

4000

3000 T ime (s)

5000

4000

5000

6000

Voltage Error

0 -0.1 0.01

-0.2

0 -0.01

-0.3 2520

1000

3000

0.1

Measured Voltage

3.2

0

(d) Voltage (V)

Voltage (V)

4000

Estimated Voltage

3.4

0.02

-20

-40

4.2

3.6

-10

-30

67

0

SOE Error

0

Reference SOE

80

(c)

10

Estimated SOE

4000

5000

6000

-0.4

2495

0

1000

2500

2000

2505

3000 T ime (s)

4000

5000

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Figure 5. Simulation results when the current sensor works properly: (a) SOE estimation results; Figure 5. Simulation results when the current sensor works properly: (a) SOE estimation results; (b) (b) SOE estimation error; (c) voltage results; (d) voltage estimation error. SOE estimation error; (c) voltage results; (d) voltage estimation error.

To determine fault to to the special situation situation To determine the the influence influence of of the the current current sensor sensor fault the SOE SOE estimation, estimation, aa special is set that the current sensor would fail at 2500 s. At this time, there will be a constant current error is set that the current sensor would fail at 2500 s. At this time, there will be a constant current error caused by the current sensor, which is set to be − 20 A in this section, as shown in Figure 6a,b,c shows caused by the current sensor, which is set to be −20 A in this section, as shown in Figure 6a,b,c shows the SOE SOE estimation estimation results results when when current current sensor sensor fault fault occurs occurs and no action action is is taken. taken. It It is is obvious obvious from from the and no the figure that the estimated SOE traces the reference SOE accurately before the current sensor fault the figure that the estimated SOE traces the reference SOE accurately before the current sensor fault occurs. At time 2500 s, when the current sensor fails without taking any action, the estimated SOE occurs. At time 2500 s, when the current sensor fails without taking any action, the estimated SOE diverges from from the the reference reference SOE SOE suddenly suddenly and and the the SOE SOE estimation estimation error error becomes becomesbigger biggerand andbigger. bigger. diverges Since then, the estimated SOE has become not so accurate, and it cannot provide as the design and Since then, the estimated SOE has become not so accurate, and it cannot provide as the design and control reference reference any control any more. more.

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measured minusreference referencecurrent; current; SOE estimation results current fault measured current current minus (c)(c) SOE estimation results whenwhen current sensorsensor fault occurs occurs and no action is taken. and no action is taken.

To reduce the influence caused by the current sensor fault, the proposed simultaneous current sensor fault detection and SOEcaused estimation is applied to the simulation and thecurrent results are To reduce the influence by the method current sensor fault, the proposed simultaneous To reduce the influence caused by the current sensor fault, the proposed simultaneous current shown in Figure 7. Figure 7a SOE is theestimation comparative profiles between the estimatedand current fault are and the sensor fault detection and method is applied to the simulation the results sensor fault detection and SOE estimation method is applied to the simulation and the results are reference fault. Figure presents the estimated SOE with the reference SOE when thethe current showncurrent in Figure 7. Figure 7a7b is the comparative profiles between the estimated current fault and shown in Figure 7. Figure 7a is the comparative profiles between the estimated current fault and sensor fails and Figure is the estimation error.SOE According to Figure 7a,when it is the found that the reference current fault.7c Figure 7bSOE presents the estimated with the reference SOE current the reference current fault. Figure 7b presents the estimated SOE with the reference SOE when the sensor fails and Figure 7c is the SOEtoestimation error. According to Figure is found thatafter the the estimated current error converges the reference current error after7a,a itshort time; current sensor fails and Figure 7c is the SOE estimation error. According to Figure 7a, it is found estimated current error converges to the reference current error after a short time; after the convergence, the estimated error traces reference trajectory accurately. It isafter clear that the estimated currentcurrent error converges to thethe reference current error after a short time; thefrom convergence, the estimated currentfault erroroccurs, traces the reference trajectory accurately. Itthe is clear from SOE Figure 7b,c, when the current sensor the estimated SOE deviates from reference convergence, the estimated current error traces the reference trajectory accurately. It is clear from Figure 7b,c, when the current fault occurs, the estimated deviates from the reference SOE suddenly. thanks to sensor the PIO based current sensor SOE fault detection method, the estimated Figure However, 7b,c, when the current sensor fault occurs, the estimated SOE deviates from the reference SOE suddenly. However, thanks to the PIO based current sensor fault detection method, the estimated SOE suddenly. converges to the reference SOE in based a short time.sensor In addition, since then, even current sensor However, thanks to the PIO current fault detection method, thethe estimated SOE SOE converges to the reference SOE in a short time. In addition, since then, even the current sensor converges to the reference SOE in a short time. In addition, since then, even the current sensor is still is still with large error, the estimated SOE could be stick to the reference SOE, which means the is still with large error, the estimated SOE could be stick to the reference SOE, which means the with large error,isthe estimated SOE could be stick to the reference SOE, which also means proposed the proposed method not only the current current sensor fault, tothe compensate proposed method is not onlyable ableto to estimate estimate the sensor fault, butbut also to compensate the method is not only able to estimate the current sensor fault, but also to compensate the fault. With such fault. With such measures, the SOE estimation is robust to the current sensor fault. fault. With such measures, the SOE estimation is robust to the current sensor fault. measures, the SOE estimation is robust to the current sensor fault.

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byby the fault is To study study more more severe severesituation situationof ofthe thecurrent currentsensor sensorfault, fault,the thecurrent currenterror errorcaused caused the fault assumed toto bebe sinusoidal is assumed sinusoidalininthe thenext nextsimulation, simulation,and andthe theresults resultsare areshown shownin inFigure Figure 8. 8. Figure 8a is the comparison between the estimated current fault and the reference current fault, and the estimated Based on Figure 8a, it could be concluded that the current sensor fault SOE is shown in Figure 8b. Based causes large largecurrent currenterror, error,which whichowns owns4040AA peak-to-peak value. However, according to figure, the figure, causes peak-to-peak value. However, according to the the the estimated current the reference error accurately, even the reference current error estimated current errorerror tracestraces to theto reference error accurately, even the reference current error changes changes sinusoidal. shows large current error, the method proposed method could sinusoidal. Figure 8bFigure shows 8b that, with that, such with largesuch current error, the proposed could ensure the ensure theofaccuracy of the SOE. estimated SOE.estimation The SOE estimation error lesseven thanthere 2% even are 40 A accuracy the estimated The SOE error is less thanis 2% are there 40 A peak-topeak-to-peak value sinusoidal current faults. peak value sinusoidal current faults. 40 Estimated Current Fault

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The ramp-type current error caused by the current sensor fault is also studied in the simulation, Theresults ramp-type currentinerror caused by results the current sensor also studied the simulation, and the are shown Figure 9. The depicted byfault the is figures indicateinthat such ramp and the results are shown in Figure 9. The results depicted by the figures indicate that such type current error could also be estimated and the SOE estimation could also be accurate. ramp type current error could also be estimated and the SOE estimation could also be accurate.

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From the simulation validation results, it can be concluded that the proposed method to From From the the simulation simulation validation validation results, results, itit can can be be concluded concluded that that the the proposed proposed method method to to simultaneously detect the current sensor fault and estimate the SOE is able to estimate accurate simultaneously simultaneously detect detect the the current current sensor sensor fault fault and and estimate estimate the the SOE SOE isis able able to to estimate estimate accurate accurate current error when current sensor fault occurs; besides, the method is also able to compensate the current current error error when when current current sensor sensor fault fault occurs; occurs; besides, besides, the the method method isis also also able able to to compensate compensate the the current sensor fault, and the influence on the SOE estimation caused by the fault can be eliminated current sensor fault, and the influence on the SOE estimation caused by the fault can be eliminated current and the influence on the SOE estimation caused by the fault can be eliminated in a in a short time, even severe situation is taken into consideration. The experimental validation with in a short severe situation is taken into consideration. The experimental validation with short time,time, eveneven severe situation is taken into consideration. The experimental validation with battery battery in loop will be discussed in the following section. battery loop be discussed in the following in loop in will be will discussed in the following section.section. 4.2. Experimental Validation for the Proposed Method 4.2.Experimental ExperimentalValidation Validationfor forthe theProposed Proposed Method Method 4.2. In this section, instead of battery model, an actual battery is utilized to experimentally validate In this this section, section, instead insteadof of battery battery model, model, an an actual actual battery battery is is utilized utilized to to experimentally experimentally validate validate In the proposed method. The experimental validation workbench is established as shown in Figure 3. the proposed proposed method. method.The Theexperimental experimentalvalidation validationworkbench workbenchisisestablished establishedasasshown shownininFigure Figure3.3. the A current sensor is utilized to obtain the current information used for the state estimation method, A current current sensor sensor is is utilized utilized to to obtain obtain the the current current information informationused usedfor forthe thestate stateestimation estimationmethod, method, A while the current information measured by the battery cycler is assumed to be true current while the measured by the cycler is assumed to be trueto current information while thecurrent currentinformation information measured bybattery the battery cycler is assumed be true current information in this study. Similar to the simulation, the normal situation when the current sensor in this study.inSimilar to the Similar simulation, thesimulation, normal situation when the currentwhen sensor works properly information this study. to the the normal situation the current sensoris works properly is firstly analyzed, and the results are shown in Figure 10. firstly properly analyzed,isand the analyzed, results areand shown in Figure works firstly the results are10. shown in Figure 10.

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Figure 10a shows the SOE estimation results when the current sensor is working properly, while Figure 10a shows the SOE estimation results when the current sensor is working properly, while the SOE estimation errorthe is shown in Figure 10b. It iswhen clear from Figure 10 that the method could get Figure 10a shows SOE estimation results the current sensor is working properly, the SOE estimation error is shown in Figure 10b. It is clear from Figure 10 that the method could get accurate even the actual the experiment. The estimated SOE traces the while the SOE SOE estimation error isbattery shown is in tested Figure in 10b. It is clear from Figure 10 that the method could accurate SOE even the actual battery is tested in the experiment. The estimated SOE traces the reference SOESOE with small and the SOE estimation is combined 2% errorSOE bound. get accurate even theerror, actual battery is tested in theerror experiment. The in estimated traces the reference SOE with small error, and the SOE estimation error is combined in 2% error bound. To emulate thesmall current sensor a voltage bias is added to the current output pins at reference SOE with error, andfault, the SOE estimation error is combined in 2%sensor error bound. To emulate the current sensor fault, a voltage bias is added to the current sensor output pins at 2500 To s. By this action, since sensor 2500 s, fault, the current used foristhe SOEtoestimation method a certain emulate the current a voltage bias added the current sensorowns output pins at 2500 s. By this action, since 2500 s, the current used for the SOE estimation method owns a certain error, which is −20 A in this study. 2500 s. By this action, since 2500 s, the current used for the SOE estimation method owns a certain error, which is −20 A in this study. no action when the current sensor fault occurs, the SOE estimation has large error as error,Ifwhich is −is 20taken A in this study. If no action is taken when the current sensor fault occurs, the SOE estimation has large error as shown in Figure 11.taken It is when obvious when the current sensorthe fault occurs at 2500has s, the estimated If no action is thethat current sensor fault occurs, SOE estimation large error as shown in Figure 11. It is obvious that when the current sensor fault occurs at 2500 s, the estimated SOE starts to deviate the reference SOE the immediately, and since then, the error shown in Figure 11. Itfrom is obvious that when current sensor fault occurs at SOE 2500 estimation s, the estimated SOE starts to deviate from the reference SOE immediately, and since then, the SOE estimation error becomes bigger and bigger. becomes bigger and bigger.

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Figure 12 12shows shows the results when the proposed proposed current sensor fault detection detection and SOE SOE Figure thethe results when the proposed currentcurrent sensor fault detection and SOE estimation Figure 12 shows results when the sensor fault and estimation methodtois isthe applied to the the experiment. experiment. The and truethe current and the the measured currentsensor with method is applied experiment. The true current measured current with current estimation method applied to The true current and measured current with current sensor fault are shown in Figure 12a. Figure 12b is the comparative profiles between the fault aresensor shown fault in Figure Figure 12b is the between the estimated current fault current are 12a. shown in Figure 12a.comparative Figure 12bprofiles is the comparative profiles between the estimated current fault and the reference current fault. Figure 12c shows the SOE estimation results and the reference fault. 12c shows SOEFigure estimation resultsthe with theestimation proposed method. estimated currentcurrent fault and theFigure reference currentthe fault. 12c shows SOE results with the proposed method. Figure 12a and its zoom figure present that the current sensor fault Figure 12a and its zoom figure present that the current sensor fault provides the SOE estimation with the proposed method. Figure 12a and its zoom figure present that the current sensor fault provides the SOE estimation method with wrong current information. However, Figure 12b shows method with wrong current information. However, Figure 12b shows that the current error12b caused by provides the SOE estimation method with wrong current information. However, Figure shows that the current error caused by the current sensor fault can be estimated accurately. The estimated the current sensor fault can be estimated accurately. The estimated current error traces the reference that the current error caused by the current sensor fault can be estimated accurately. The estimated current fault errorwell, traces the when reference current fault well,ateven even when there is− step change at 2500 2500current from current even therecurrent is a step change 2500when s fromthere 0 A to A.change The estimated current error traces the reference fault well, is aa 20 step at ss from 0 A to −20 A. The estimated current fault converges to the reference current fault in a short time, to the reference current fault in a short which provides proposed method 0fault A toconverges −20 A. The estimated current fault converges to time, the reference current the fault in a short time, which provides the proposed method accurate information to compensate it. However, compared accurate information to compensate it. However, compared with the simulation results in Figure 7, which provides the proposed method accurate information to compensate it. However, compared with the simulation results in Figure 7, the estimated error ripple is bigger when the actual battery is the estimated error ripple actual battery is applied, which is believed to be caused with the simulation resultsisinbigger Figurewhen 7, thethe estimated error ripple is bigger when the actual battery is applied, whichmodeling is believed believed to be be caused caused by by the the battery battery modeling modeling error. error. by the battery error. applied, which is to (b) (b)

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As shown shown in in the the figure, figure, the the current current sensor sensor fault fault detection detection and and SOE SOE estimation estimation method method is is realized realized As simultaneously, and the estimation is accurate. Similar to the simulation results, the estimated SOE simultaneously, and the estimation is accurate. Similar to the simulation results, the estimated SOE traces to the reference SOE accurately as shown in Figure 10c. When the current sensor fault occurs, traces to the reference SOE accurately as shown in Figure 10c. When the current sensor fault occurs, the estimated estimated SOE SOE deviates deviates from from the the reference reference SOE SOE aa little, little, and and in in aa short short time, time, the the estimated estimated SOE SOE the converges to the reference SOE. The maximum SOE estimation error is less than 2%, which exists converges to the reference SOE. The maximum SOE estimation error is less than 2%, which exists

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As shown in the figure, the current sensor fault detection and SOE estimation method is realized simultaneously, and the estimation is accurate. Similar to the simulation results, the estimated SOE traces to the reference SOE accurately as shown in Figure 10c. When the current sensor fault occurs, the estimated SOE deviates from the reference SOE a little, and in a short time, the estimated SOE converges to the reference SOE. The maximum SOE estimation error is less than 2%, which exists exactly the time when the current sensor fault occurs. Henceforth, even the current sensor is still with large error, the estimated SOE sticks to the reference SOE. 5. Conclusions A method to simultaneously detect the current sensor fault and estimate the SOE for batteries in EVs has been proposed in this paper. The simplified battery model was firstly introduced and analyzed. Secondly, the PIO based current sensor fault detection and SOE estimation method was proposed. The convergence of fault detection and state estimation has been proved. In order to give the efficiency of the proposed method without modeling error influence, the simulation of the proposed method was established first. The current error caused by the current sensor fault could be estimated accurately, and the SOE of the batteries could be obtained effectively. To further verify the proposed method, a battery test workbench was established and the proposed method was applied to an actual battery used in EVs. Through implementing the experiments, acceptable accuracy of the fault estimation and the SOE estimation has been verified. The current error caused by the current sensor fault could be accurately estimated, even when the error was severe. The influence caused by the current sensor fault could be eliminated in a short time and the biggest SOE estimation error was as small as 2%. Acknowledgments: This work was supported by the National Natural Science Foundation of China (Grant No. 51405374), the Postdoctoral Science Foundation of China (Grant No. 2014M560763), the Postdoctoral Science Special Foundation of China (Grant No. 2016T90904), the Fundamental Research Funds for the Central Universities and Postdoctoral Science Foundation of Shaanxi. Author Contributions: Jun Xu and Binggang Cao designed the overall algorithms and the simulations; Shiying Li and Jing Wang designed and performed the experiments; Jun Xu and Shiying Li analyzed the data and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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