energies Article
Insulation Resistance Monitoring Algorithm for Battery Pack in Electric Vehicle Based on Extended Kalman Filtering Chuanxue Song 1 , Yulong Shao 1 , Shixin Song 2 , Silun Peng 3 , Fang Zhou 3 , Cheng Chang 3 and Da Wang 1, * 1 2 3
*
State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun 130022, China;
[email protected] (C.S.);
[email protected] (Y.S.) School of Mechanical Science and Engineering, Jilin University; Changchun 130022, China;
[email protected] Department of Automotive Engineering, College of Automotive Engineering, Jilin University, Changchun 130022, China;
[email protected] (S.P.);
[email protected] (F.Z.);
[email protected] (C.C.) Correspondence:
[email protected]; Tel.: +86-159-4802-3961
Academic Editor: Rui Xiong Received: 16 March 2017; Accepted: 12 May 2017; Published: 18 May 2017
Abstract: To improve the accuracy of insulation monitoring between the battery pack and chassis of electric vehicles, we established a serial battery pack model composed of first-order resistor-capacitor (RC) circuit battery cells. We then designed a low-voltage, low-frequency insulation monitoring model based on this serial battery pack model. An extended Kalman filter (EKF) was designed for this non-linear system to filter the measured results, thus mitigating the influence of noise. Experimental and simulation results show that the proposed monitoring model and extended Kalman filtering algorithm for insulation resistance monitoring present satisfactory estimation accuracy and robustness. Keywords: insulation resistance; first-order resistor-capacitor (RC) circuit; battery pack model; extended Kalman filtering (EKF); electric vehicle
1. Introduction The voltages of storage batteries, fuel cells, and ultra-capacitors for electric vehicles far exceed the safety limit for the human body, with certain battery packs reaching voltages of 600 V. The performance of insulating materials, however, degrades after a certain period. Other factors, such as humidity, can also decrease the performance of the insulation between a high-voltage system and the chassis ground. Such decrease will create a leakage circuit when the positive or negative wire penetrates the insulating layer and connects to the chassis ground, which increases its electric potential and thus affects the operation of the motor controller, other low-voltage electronics, and passengers’ safety. When insulation performance is degraded in multiple points between the high-voltage circuit and the chassis ground, heat energy accumulates, which may cause electrical fires under serious circumstances. To ensure safe vehicle operation, a specialized device should be designed for the real-time online monitoring of insulation resistance between the high-voltage system and the chassis ground [1,2]. Current methods for monitoring insulation within electric vehicles all have significant drawbacks. The two most prevalent methods, namely, balanced bridge circuit [3,4] and the unbalanced bridge circuit [5], cannot detect leakage between the battery pack and the chassis ground. Furthermore, the introduction of reference resistance during measurement reduces the insulation performance of the system. The accuracy of non-contact current differential detection [6] for insulation monitoring Energies 2017, 10, 714; doi:10.3390/en10050714
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Pack Voltage Pack Voltage (V)(V)
performance of the system. The accuracy of non-contact current differential detection [6] for performance of therequires system.further The accuracy of non-contact current differential detection [6] for in electric vehicles improvement. Although the alternating current (AC)-voltage insulation monitoring in electric vehicles requires further improvement. Although the alternating insulation monitoring in electric vehicles requires further improvement. Although the alternating signal method [7] injection mitigatesmethod the interference of electromagnetic of a vehiclesignals to the currentinjection (AC)-voltage signal [7] mitigates the interference signals of electromagnetic current (AC)-voltage signal injection method [7] mitigates the interference of electromagnetic signals monitoring the frequentcircuit, injection high-voltage signals affects the safe operation battery of a vehicle circuit, to the monitoring theoffrequent injection of high-voltage signals affectsofthe safe of a vehicle to the monitoringthe circuit, the frequent injection of high-voltage affects the safe packs. In addition, proposed low-voltage, low-frequency signalsignals injection method can operation of batteryalthough packs. In addition, although the proposed low-voltage, low-frequency signal operation of battery packs. In addition, although the proposed low-voltage, low-frequency signal detect leakage within the battery pack, mismeasurement may occur during voltage spikes. To improve injection method can detect leakage within the battery pack, mismeasurement may occur during injection method can detect leakage within theinbattery pack,study, mismeasurement may occur the accuracy of dynamic insulation monitoring, the present measurement and systemduring noise voltage spikes. To improve the accuracy of dynamic insulation monitoring, in the present study, voltage spikes. To improve the accuracy of dynamic insulation monitoring, in the present study, were considered based on the low-voltage, low-frequency signal injection method, and the insulation measurement and system noise were considered based on the low-voltage, low-frequency signal measurement andbattery system noise considered based themodel, low-voltage,were low-frequency signal monitoring of the waswere modeled. On the basis ofon this filtered according injection method, and thepack insulation monitoring of the battery pack wasresults modeled. On the basis of this injection method, and the insulation monitoring the batteryresults pack was modeled. On theapproximate basis of this to the extended Kalman filtering algorithm soextended thatofcalculation would most closely model, results were filtered according to the Kalman filtering algorithm so that calculation model, results were filtered according to the extended Kalman filtering algorithm so that calculation actual resistance. resultsinsulation would most closely approximate actual insulation resistance. results would most closely approximate actual insulation resistance. 2. Mechanism of of the the Low-Voltage, Low-Voltage, Low-Frequency 2. Mechanism Low-Frequency Signal Signal Injection Injection Method Method Monitoring Monitoring Circuit Circuit 2. Mechanism of the Low-Voltage, Low-Frequency Signal Injection Method Monitoring Circuit Figure shows the the overall overall voltage voltage curve of the the battery battery pack pack of of an an electric electric vehicle vehicle during during realistic realistic Figure 11 shows curve of Figure 1 shows the overall voltage curve ofEthe battery packacceleration of an electric vehicle during realistic working conditions. In this figure, A to B and to F are hard processes, whereas C to working conditions. In this figure, A to B and E to F are hard acceleration processes, whereas C to D working conditions. In this figure, A to B and E to F are hard acceleration processes, whereas C to in D D and G to H are regenerative braking processes. During these processes, the violent fluctuation and G to H are regenerative braking processes. During these processes, the violent fluctuation in the andoverall G to H voltage are regenerative processes. Duringthe these processes, the violent fluctuation in the the asbraking high 80To V. analyze To analyze effect of changes in the overall voltage of overall voltage can can be asbehigh as 80asV. the effect of changes in the overall voltage of the overall voltage can be as high as 80 V. To analyze the effect of changes in the overall voltage of the the battery pack monitoring accuracy, equivalent circuitmodel modelofofthe thebattery battery pack pack should should be battery pack on on monitoring accuracy, thethe equivalent circuit be battery pack on monitoring accuracy, the equivalent circuit model of themonitoring battery pack should be considered in the insulation monitoring model. The insulation resistance model of the considered in the insulation monitoring model. The insulation resistance monitoring model of the considered the insulation monitoringvia model.low-voltage, The insulation resistance monitoring model of the battery packin(Figure (Figure 2) can signal injection injection method, battery pack 2) can be be acquired acquired via the the low-voltage, low-frequency low-frequency signal method, battery pack (Figure 2) can be acquired via the low-voltage, low-frequency signal injection method, where: E11−E −E arethe the open-circuit voltages battery cells; r01 −r0nthe areinternal the internal resistances; where: E n n are open-circuit voltages of of thethe battery cells; r01−r 0n are resistances; r1−rn where: E 1−E n are the open-circuit voltages of the battery cells; r 01−r0n are theRinternal resistances; r1−rn rare − r are the polarized resistances; C − C are the polarized capacitors; − R are the insulation n n n 1 the polarized resistances; C1−Cn are1 the polarized capacitors; R0−Rn are the 0 insulation resistances are the polarized resistances; C1−Cinn are theand polarized capacitors; R0I−R arebus the insulation resistances resistances batteries series the chassis ground; isnthe the battery between thebetween batteriesthe in series and the chassis ground; I is the bus current of thecurrent batteryof pack; Rr1 and between the batteries in series and the chassis ground; I is the bus current of the battery pack; Rr1 and pack; R and R are the reference resistances of the monitoring circuit (with both values being r1 r2 r ); Rr2 are the reference resistances of the monitoring circuit (with both values being Rr); Rs is R the Rsr2isare the reference resistances off isthe monitoring circuit (with both values being Rr); Rs is the R the sampling resistance; and E the square-wave generator. sampling resistance; and Ef is the square-wave generator. sampling resistance; and Ef is the square-wave generator. 400 400 380 380 360 360 340 340 320 320 300 300 280 280 0 0
H H D D A AC C B B
E E
G G
F
50 F 50
100
150 150
100/s Time Time /s
200 200
Figure 1. Total voltage curve curve of the the battery pack. pack. Figure Total voltage Figure 1. 1. Total voltage curve of of the battery battery pack.
E1 E1 R0 R0
Rr1 Rr1
C1 C1 r1 r1
E2 E2
... ...
C2 C2 r2 r2
R1 R1
En En R(n-1) R(n-1)
Ef Ef
Cn Cn rn rn Rn Rn
Rr2 Rr2
Rs Rs
Figure 2. Insulation detection model between the battery and chassis of an electric vehicle. Figure 2. Insulation detection model between the battery and chassis of an electric vehicle. Figure 2. Insulation detection model between the battery and chassis of an electric vehicle.
The maximum leakage current occurs at either the positive or negative electrode of the battery The maximum leakage current occurs at either the positive or negative electrode of the battery pack. Thus, the insulation resistance of the two electrodes should be monitored to determine the pack. Thus, the insulation resistance of the two electrodes should be monitored to determine the
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The maximum leakage current occurs at either the positive or negative electrode of the battery 3 of 13 pack. Thus, the insulation resistance of the two electrodes should be monitored to determine the insulation performance performance of of the the battery battery pack. pack. The The insulation insulation resistances resistances of of the the positive positive and and negative insulation negative electrodes are defined as R and R respectively. Therefore, p n electrodes are defined as Rp and Rn respectively. Therefore, Energies 2017, 10, 714
RpR=1 //R R1//R2 2.…//R n, n , Rp = . . //R and, and, RRnn == R00.
The insulation resistance monitoring monitoring circuit of the positive electrode Rpp can can be simplified as shown in Figure 3, where EH is the terminal terminal voltage voltage of the the battery battery pack, pack, V Vff is the low-voltage monitoring monitoring square-wave square-wave voltage, voltage, and Vss is is the the voltage of the sampling resistance. The monitoring voltage generates generatesaamonitoring monitoringcurrent current that flows sampling resistance. Then, the squarethat flows intointo the the sampling resistance. Then, the square-wave wave voltage generated from the sampling resistance is measured and converted bycontrol the control voltage signalsignal generated from the sampling resistance is measured and converted by the unit unit in accordance with Equation (6). The value of insulation resistance will be calculated within in accordance with Equation (6). The value of insulation resistance will be calculated within the control unit. Vh I1
EH I2
Rr1
Rr2
Rp Vf Ef
Vs Rs
Is
Figure Figure 3. 3. Principle Principle of of monitoring monitoring insulation insulation resistance resistance between between the the positive positive electrode electrode and and the the chassis. chassis.
Equation (6) can be acquired via the following steps: Equation (6) can be acquired via the following steps:
I2 = I1 + Is
(1) (1) Vf = Rp × I s + Rr 2 × I2 + Rs × I s (2) Vf = R p × Is + Rr2 × I2 + Rs × Is (2) Vh = Rr1 × I1 + Rr2 × I2 (3) Vh = Rr1 × I1 + Rr2 × I2 (3) where Vs can be measured through the voltage measuring circuit. Therefore, Is can be expressed where Vs can be measured through the voltage measuring circuit. Therefore, Is can be expressed through Equation (4). The correlation between Rr1 and Rr2 can be expressed as Equation (5). through Equation (4). The correlation between Rr1 and Rr2 can be expressed as Equation (5). I2 = I1 + Is
Is = Vs Rs
(4) (4) Rr1 = Rr2 = Rr (5) Rr1 = Rr2 = Rr (5) Therefore, through conversion, the insulation resistance between the positive electrode and the Therefore, through conversion, the insulation resistance between the positive electrode and the chassis ground is: chassis ground is: − VVhh 2 ×VVf f − 2× R pR=s × Rs × −−RR × R× 0.50.5 Rp = (6) (6) s− s − r Rr 2 2××Vs Is = Vs /Rs
3. Design of the Discrete Extended Kalman Filter 3. Design of the Discrete Extended Kalman Filter The extended Kalman filter (EKF) was designed during system modeling to reduce the impact of The extended filterThe (EKF) was designed system modeling to reduce theefficient impact the overall voltage Kalman fluctuation. extended Kalmanduring filtering algorithm includes a highly of the overall voltage fluctuation. The extended Kalman filtering algorithm includes a highly efficient observer, which also presents high robustness against non-linear systems [8,9]. To apply the EKF in observer, which also presents high robustness against non-linear systems [8,9]. To apply the EKF in the insulation monitoring system, the system should be described by a state space model [10], which can be expressed as:
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the insulation monitoring system, the system should be described by a state space model [10], which can be expressed as: X(k + 1) = f[k, X(k)] + G(k) × W(k) (7) Z (k ) = h[k, X(k)] + V(k)
(8)
where X(k + 1) and X(k) are the respective system state vectors at the kth and (k + 1)th sampling time; G(k) is the noise-driving matrix; W(k) is the process noise; V(k) is the observation noise; and f[k, X(k )] and h[k, X(k)] are functions that describe the system. In the mode of the insulation monitoring system proposed in this paper, X(k) = [Vh (k) Vs (k)]T . Thus, f[k, X(k)] = X(k)
(9)
Vf × R S A × X( k ) × R S − − RS − 0.5 × Rr (10) B × X( k ) B × X( k ) h i h i h iT where A = 1 0 , B = 0 1 and X(k ) = Vh Vs . Given that the system is nonlinear, a linearization process is undertaken at each step to approximate a nonlinear system with a linear time-varying system [11]: h[k, X(k)] =
X(k + 1) = F( k + 1| k )X( k ) + G( k ) × W( k ) + Φ ( k ) ∧ ∧ ∂h X k − X k k − 1 + V( k ) Z( k ) = h X( k | k − 1), k + ∧ ( ) ( ) | ∧ ∂ X ( k ) X( k | k −1) where,
∂h ∧ ∂X( k ) ∧
(11)
(12)
= H(k)
X( k | k −1)
∂h h X( k | k − 1), k − ∧ ∂X( k ) ∧
∧
∧
X( k | k − 1) = y( k )
X( k | k −1)
Therefore, Equation (12) can be expressed as: Z ( k ) = H( k )X( k ) + y ( k ) + V( k )
(13)
The linearized model is then acquired as: X( k + 1) = F( k + 1| k )X( k ) + G( k ) × W( k )
(14)
Z ( k ) = H( k )X( k ) + y ( k ) + V( k )
(15)
where, F( k + 1| k ) = 1 , G(k ) is the noise-driven matrix, W(k) is the process noise with an average value of 0 and a variance of Q, and V(k) is white Gaussian noise with an average value of 0 and a variance of R. H( k ) =
− Rs 2 ×Xk −1 (2 )
R s ( −2 × Vf +Xk −1 (1 ) ) 2×(Xk−1 (2))2
(16)
The choice of covariance matrices affects the filter convergence and should thus be considered with care. In practice, process and measurement noises Q and R are difficult to obtain [12]. Therefore,
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they are often used as tuning parameters. Laroche et al. [13] proposed a methodology for tuning Q to achieve parameter tracking. The component of the matrix is chosen as the square of the typical parameter variation on a sampling interval. To ensure convergence in less than being h 40 s and without i
too senstive to the noise, after measurement and multiple adjustment, Q = 0.04 0.01 and R = 80 are chosen. EKF is essentially based on the principle of minimizing the mean square error estimation to seek a recursive estimation algorithm. The time update and measurement update are consecutively performed at each time interval. The detailed steps can be summarized by the following steps [14,15]: (1) (2)
Initial state X(0) and P0 . Time update, which includes the state space update and covariance of the error update: ˆ
(3)
X− k = Xk −1
(17)
T ˆ P− k = Fk Pk −1 Fk + Qk
(18)
− ˆ where X− k is the predicted state at step k, Xk −1 is the previous estimated state at step k−1, Pk is the predicted error covariance at step k, and Pˆ k−1 is the estimated error covariance at step k−1. Measurement update, which involves Kalman gain calculation, state estimation measurement update, and error covariance update:
h i −1 T − T Kk = P− k × Hk × Hk × Pk × Hk
(19)
− Z− k = Hk × Xk
(20)
− Xˆ k = X− k + K × (Zk − Zk )
(21)
Pˆ k = (I − Kk × Hk ) × P− k
(22)
where Kk is the Kalman gain, Z− k is the predicted output, and Zk is the measured output. 4. Matlab Simulation Model and Analysis 4.1. Simscape Battery Cell Model Several battery models and charging and discharging characteristics were described in references [16–19]. The first-order equivalent circuit model is very common in simulating cell voltage change because the model is relatively simple, can easily obtain parameters, and runs in real time. The core goal of the equivalent circuit model is to simulate the actual battery voltage response of the current input. Huria et al. [20] reported that the first-order resistor-capacitor (RC) circuit model is precise for most industrial application. Increasing the order will significantly increase the amount of required calculation, but will not increase accuracy [21]. The first-order equivalent circuit model is supported by Huria et al. [20] due to its accuracy and feasibility, and many researchers have adapted this model in their studies [18,22–25]. Figure 4 shows the classic first-order RC equivalent circuit model. The equivalent circuit model, which contains a voltage source, series resistor, and a pair of RC, accurately describes cell characteristics. The electrical behavior of a practical model [26] shown in Figure 4 can be expressed as follows: •
U1 = −
U1 I + L R1 C1 C1
Ut = Em − U1 − IL R0
(23) (24)
precise for most industrial application. Increasing the order will significantly increase the amount of required calculation, but will not increase accuracy [21]. The first-order equivalent circuit model is supported by Huria et al. [20] due to its accuracy and feasibility, and many researchers have adapted this model in their studies [18,22–25]. Figure 4 shows the classic first-order RC equivalent circuit Energies 714 6 of of 13 model.2017, The10, equivalent circuit model, which contains a voltage source, series resistor, and a pair RC, accurately describes cell characteristics.
R1 R0 + + Em
C1
Figure circuit model. model. Figure 4. 4. First-order First-order resistor-capacitor resistor-capacitor (RC) (RC) equivalent equivalent circuit
In Figure 4, Em is the open circuit voltage; R1 and C1 are the resistance and capacitance of polarization effect respectively, and R0 represents the resistance of battery. Em , R1 , C1 , and R0 are functions of the state of charge (SOC) and temperature. Specifically, these four elements can be obtained from the two-dimensional look-up tables: R0 = R0 (SOC, T)
(25)
R1 = R1 (SOC, T)
(26)
C1 = C1 (SOC, T)
(27)
Em = Em (SOC, T)
(28)
Those look-up tables were obtained by using a parameter estimation tool in Simulink Design Optimization (R2012b, The MathWorks, Inc, Natick, MA, USA) with series pulse discharge data under different temperatures. These look-up tables were selected based on seven different points of SOC. The pulse discharge curve for each temperature was run individually through estimation. This will produce a set of one-dimensional look-up tables versus SOC for the four parameters at each temperature. Simulink Design Optimization iteratively simulated the discharge profile in Simscape while comparing the simulation results with experimental data. Then also, using nonlinear least squares algorithm, the error gradient across each of the 28 parameters (four tables × seven breakpoints) to minimize the sum of squared error. We used the battery model from reference [20], which is a fidelity electrical model with thermal dependence, to characterize and simulate high-power lithium battery cells. Hence, the SOC and temperature were calculated following the method cited in the literature. SOC was calculated in Coulomb counting using Equation (29), and SOC(t0 ) was periodically recalibrated by the SOC-OCV (open circuit voltage) curve. State of health (SOH) was calculated using Equations (30) and (31) as follows: Z SOC(t) = SOC(t0 ) − ( I(t) dt)/CM , (29) CM = (PassedCharge)/(SOC2 − SOC1 ),
(30)
SOH = CM /CN × 100%,
(31)
where SOC(t0 ) is the SOC at the beginning of the discharge or charge; I(t) is the working current; CM is the current capacity of the battery; CN is the brand new capacity of the battery; PassedCharge is the total capacity flow out of the battery; and SOC1 and SOC2 are the SOCs of the battery before and after discharge, respectively. Thermal influence is not usually considered in the currently proposed battery models. However, Huria et al. [20] added a thermal model to the equivalent circuit model and creatively improved the Simscape model. As shown in Figure 5, the Simscape model contains three input terminals (environment temperature input, positive, and negative) and three output terminals (battery temperature, SOC, and energy consumption power).
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These outputs can be used to analyze the operating state of the cell and estimate the system insulation resistance. The Simscape model is suitable for Matlab simulation and analysis. The parameters of the equivalent circuit model can be estimated through the least square method with Energies 2017, 10, 714 7 of 13 experimental data, which can be obtained by pulse discharge process under different temperatures and SOCs. Then, the parameter results are incorporated into look-up tables that are related to SOC and Wang et al. [27]. Their results indicate that the model responds accurately in a given battery voltage Energies 2017, 10, 714 13 is a temperature T. The computer determines the parameters of the model via the look-up tables.7 of This fluctuation. practical method. Moreover, the Simscape model has been tested by Huria et al. [20] and Wang et al. [27]. Wang et al. [27]. Their results indicate that the model responds accurately in a given battery voltage Theirfluctuation. results indicate that the model responds accurately in a given battery voltage fluctuation.
Figure 5. Simscape first-orderRC RCequivalent equivalent circuit. Figure 5. Simscapemodel modelof of the the first-order circuit. Figure 5. Simscape model of the first-order RC equivalent circuit.
4.2. Battery Model 4.2. Battery PackPack Model 4.2. Battery Pack Model were connected seriesto tocompose compose aa stack 6).6). The internal structure of each EightEight cellscells were connected ininseries stack(Figure (Figure The internal structure of each battery is shown in Figure 5, where the H terminal outputs the internal temperature of the battery, Eight cells were connected in series a stack (Figure 6). The internal structure of each battery is shown in Figure 5, where the to H compose terminal outputs the internal temperature of the battery, and transfer occurs between two batteries simulate the heat transferof onthe both sides and battery isconvective shownheat in heat Figure 5, where H terminal outputs to the internal temperature and convective transfer occursthe between two batteries to simulate the heat transfer onbattery, both sides of the battery. The m-port on each battery outputs the collected battery voltage, current, andof the convective heat transfer occursonbetween two batteries to simulate the heat transfer on bothcurrent, sides of the battery. The m-port each battery outputs the collected battery voltage, and temperature. Next, 10 stacks were again connected in series to compose a pack (Figure 7). The model battery. The m-port onstacks each battery outputs the collected battery voltage, current, and7). temperature. temperature. Next, 10 were again connected in series to compose a pack (Figure The model parameters are derived from 80 ICR18650 battery cells (Samsung SDI Co., Ltd., Yongin-Si, GyeonggiNext, 10 stacks were again connected in series to compose a packSDI (Figure 7). The model parameters parameters are derived 80 ICR18650 cells (Samsung Co.,battery Ltd., Yongin-Si, GyeonggiDo, Korea) using thefrom method in [20]. Thebattery discharge capacity of the series pack is limited by are derived from 80 ICR18650 battery cells (Samsung SDI Co., Ltd., Yongin-Si, Gyeonggi-Do, Korea) Do, Korea) the method in [20]. The discharge capacity of value the series is limited by the cell using with the smallest SOC. Therefore, we make the minimum of thebattery SOCs ofpack all series cells using the method in [20]. The discharge capacity of the series battery pack is limited by the cell with as the SOC of the battery pack. Similarly, the SOH of the battery pack is the minimum of the series the cell with the smallest SOC. Therefore, we make the minimum value of the SOCs all series cells the smallest SOC. we make the minimum value the SOCs cells asofthe of cells’ as the SOCSOHs. of the Therefore, battery pack. Similarly, the SOH of the of battery packofisall theseries minimum theSOC series the battery cells’ SOHs.pack. Similarly, the SOH of the battery pack is the minimum of the series cells’ SOHs.
Figure 6. Eight cells connected in series to compose a stack.
Through the charging and discharging process of the 80 battery cells, we validated the accuracy Figure 6.actual Eight cells connected connected inaseries series to compose compose stack. of our model relativeFigure to the6. We built 3.2-Ah, 296-V battery pack model composed Eightreaction. cells in to aa stack. of 80 battery cells that were connected in series. When the pack is fully charged, the voltage can reach Through the8charging discharging the 80 battery cells, we validated the 336 V. Figure comparesand the battery voltageprocess betweenofthe simulation and experimental results foraccuracy the battery under (a) actual constant current/constant (CC/CV) charging mode, and composed a (b) of our modelpack relative toathe reaction. We built avoltage 3.2-Ah, 296-V battery pack model C/1 Ccells discharging mode. The simulation results closely approximate experimental valuescan andreach of 80 0.5 battery that were connected in series. When the pack is fully the charged, the voltage
336 V. Figure 8 compares the battery voltage between the simulation and experimental results for the battery pack under a (a) constant current/constant voltage (CC/CV) charging mode, and a (b)
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Through the charging and discharging process of the 80 battery cells, we validated the accuracy of our model relative to the actual reaction. We built a 3.2-Ah, 296-V battery pack model composed of 80 battery cells that were connected in series. When the pack is fully charged, the voltage can reach 336 V. Figure 8 compares the battery voltage between the simulation and experimental results for theEnergies battery pack under a (a) constant current/constant voltage (CC/CV) charging mode, and a (b) 2017, 10, 714 8 of 13 Energies 2017, 10, 714 8 of 13 0.5 C/1 C discharging mode. The simulation results closely approximate the experimental values and have a maximum thatthe thebattery batterypack packmodel model accurately reflects have a maximumerror errorofof1.6%. 1.6%.These These results results showed showed that accurately reflects have a maximum error of 1.6%. These results showed that the battery pack model accurately reflects thethe actual voltage and monitoringof ofthe thepower powersystem. system. actual voltage andcan canbebeapplied appliedin inthe the insulation insulation monitoring the actual voltage and can be applied in the insulation monitoring of the power system.
Figure 7.Ten Tenstacks stacks connected connected in series compose aapack. Figure seriestoto tocompose compose pack. Figure 7. 7. Ten stacks connected ininseries a pack.
300 300 280 280 260 260 240 240 220 220 200 200 0 0
Experiment Experiment Simulation Simulation
290 290 288 288 286 286 284 284 282 282 280 280 100 200 300 400 500 100 200 300 400 500 1000 2000 3000 4000 5000 6000 1000 2000 3000 4000 5000 6000 Time (s)
Time (s)
340 340 320 320 300 300 290 280 290 280 285 260 285 280 260 280 240 275 240 275 220 270 220 270 7000 7500 200 7000 7500 0 2000 4000 6000 8000 200 0 2000 4000 6000 8000 Time (s)
Battery voltage (V)(V) Battery voltage
Battery voltage (V)(V) Battery voltage
340 340 320 320
Experiment Experiment Simulation Simulation
10000 12000 10000 12000
Time (s)
(a) (b) (a) (b) Figure 8. Verification of the battery pack model: (a) Experimental and simulation charge curves under Figure 8. Verification of the battery pack model: (a) Experimental and simulation charge curves under Figure 8. Verification of the voltage battery (CC/CV) pack model: (a) Experimental and simulation charge curves under constant current/constant charging mode; (b) Experiment and simulation discharge constant current/constant voltage (CC/CV) charging mode; (b) Experiment and simulation discharge curves current/constant under 0.5 C/1 C discharging mode. charging mode; (b) Experiment and simulation discharge constant voltage (CC/CV) curves under 0.5 C/1 C discharging mode. curves under 0.5 C/1 C discharging mode.
4.3. Insulation Resistance Monitoring Model 4.3. Insulation Resistance Monitoring Model 4.3. Insulation Resistance model Monitoring Model in Figure 9. In the model, vehicle speed and ambient The monitoring is shown The monitoring model is shown in Figure 9. In the model, vehicle speed and ambient temperature were simulated by Signal Builder. The power system of the vehicle was also temperature simulated The monitoring model is by shown in Builder. Figure 9.The In the model, vehicle speed andwas ambient temperature were simulated Signal power system of the vehicle also simulated through the vehicle transmission system, which calculated the current through the battery pack. R01 were simulated by Signal Builder.system, The power of the also simulated through the vehicle transmission whichsystem calculated thevehicle currentwas through the battery through pack. R01 the and R02 are the reference resistances, Rs is the sampling resistance, and Rp is the insulation resistance vehicle system, which calculated the current through the pack. R01resistance and R02 are and R02transmission are the reference resistances, Rs is the sampling resistance, and Rpbattery is the insulation between the simulated battery pack and the chassis ground. In Figure 9a, the Vf signal waveform is the reference Rs is the resistance, andInRpFigure is the9a, insulation resistance between between the resistances, simulated battery packsampling and the chassis ground. the Vf signal waveform is drawn to express the Vf signal more clearly, with a signal voltage of ±40 V and a frequency of 0.25 the simulated battery pack and the chassis ground. In Figure 9a, the V signal waveform is drawn drawn to express the Vf signal more clearly, with a signal voltage of ±40 V f and a frequency of 0.25 Hz. The Figure 9b shows that the extended Kalman filtering algorithm was achieved by the EKF toHz. express the Vf9b signal more with aKalman signal voltage ±40 V and frequency of 0.25 The Figure shows that clearly, the extended filtering of algorithm was a achieved by the EKF Hz. block. In the simulation experiment, the variances of the noises added to VH and Vs signals are 0.02 block. In the the Kalman variancesfiltering of the noises addedwas to Vachieved H and Vs signals The Figure 9b simulation shows thatexperiment, the extended algorithm by the are EKF0.02 block. and 0.00001 respectively and the measure noise is 80 or 800. and 0.00001 respectively and the measure noise is 80 or 800. In the simulation experiment, the variances of the noises added to V H and Vs signals are 0.02 and In the simulation, R01 = 2000 KΩ, R02 = 2000 KΩ, and RS = 10 KΩ, and the NEDC operating cycle Inrespectively the simulation, Rthe 01 = measure 2000 KΩ, noise R02 = 2000 KΩ, and RS = 10 KΩ, and the NEDC operating cycle 0.00001 and is 80 or 800. was simulated. The system impedance was set as 2000 KΩ and 20 KΩ. The variance of the simulation wasInsimulated. The system impedance set as 2000 and KΩ. The variance of theoperating simulation KΩ,results Rwas 2000 KΩ, KΩ and RS =20 and the NEDC cycle 01 =802000 02 = are noisethe wassimulation, set as 4000 R and K. The shown in Table 1.10AKΩ, comparison of simulations 1 and noise was set as 4000 and 80 K. The results are shown in Table 1. A comparison of simulations 1 and was The systemthat impedance was setcircuit as 2000 KΩ andthe 20 KΩ. The variance ofregardless the simulation 2, simulated. or of 3 and 4, revealed the monitoring calculates insulation resistance of 2, orwas of 3 set andas 4, 4000 revealed that the monitoring circuit calculates the insulation resistance regardless 1ofand noise and 80 K. The results are shown in Table 1. A comparison of simulations the value of system impedance and the variance of noise. In addition, EKF effectively reduced the value of 4, system impedance and the variance of noise. In addition, EKF effectively reduced the 2,the or of 3 and revealed circuit calculates the insulation resistance regardless maximum absolute errorthat andthe themonitoring root mean square error. A comparison of simulations 1 and 3, or of of maximum absolute error and the root mean square error. A comparison of simulations 1 and 3, or of the2 value system impedance and theKalman variance of noise. In addition, EKF improves effectivelymonitoring reduced the and 4,ofrevealed that the extended filtering algorithm markedly 2 and 4, revealed that the extended Kalman filtering algorithm markedly improves monitoring accuracy when the system is suffering from degraded insulation performance. accuracy when the system is suffering from degraded insulation performance.
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maximum absolute error and the root mean square error. A comparison of simulations 1 and 3, or of 2 and 4, revealed that the extended Kalman filtering algorithm markedly improves monitoring accuracy when the system is suffering from degraded insulation performance. Energies 2017, 10, 714 9 of 13
(a)
(b) Figure 9. Simulink model of insulation detection: (a) The overall model of the detection circuit; Figure 9. Simulink model of insulation detection: (a) The overall model of the detection circuit; (b) The (b) The Simulink model of the extended Kalman filter (EKF) and the noise. Simulink model of the extended Kalman filter (EKF) and the noise. Table 1. Results of the simulation. RF: Reference Resistor.
Table 1. Results of the simulation. RF : Absolute ReferenceError Resistor. Maximum Root Mean Square Error Simulation System Impedance Measure Noise (Ω) (Ω) No. RF (KΩ) Variance Maximum Absolute Error (Ω) Root Mean Square Error (Ω) System Impedance Measure Noise without EKF with EKF without EKF with EKF Simulation No. RF (KΩ) Variance without EKF with EKF without EKF with EKF 1 2000 800 4780.3 1426.4 1974.5 589.7 12 2000 4780.3 1426.4 1974.5 589.7 2000 80800 723.7 205.6 277.3 77.9 2 2000 80 723.7 205.6 277.3 77.9 3 20 800 4780.3 427.8 1879.1 206.4 3 20 800 4780.3 427.8 1879.1 206.4 2020 8080 723.7 143.9 256.2 38.5 44 723.7 143.9 256.2 38.5
5. Analysis of Bench Test Results To validate the superiority of the proposed model and the algorithm based on extended Kalman filtering, the insulation monitoring circuit based on this study was tested in an actual battery pack
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5. Analysis of Bench Test Results To validate the superiority of the proposed model and the algorithm based on extended Kalman filtering, the insulation monitoring circuit based on this study was tested in an actual battery Energies 2017, 10, 714 10 of 13 pack Energies 2017, 10 10, 714 10 ofbattery 13 system. Figure shows the 52-Ah, 296-V battery pack system, which was composed of 1600 system. Figure shows thefor 52-Ah, 296-V battery pack system, which of 1600 battery cells (ICR18650 3.710 V/2.6 Ah) the bench test. Within this pack, 20was cellscomposed were connected in parallel system. Figure 10 shows the 52-Ah, system, which waswere composed of 1600 battery cells (ICR18650 V/2.6 Ah) for the 296-V benchbattery test. Within this pack, 20 cells connected parallel as a stack, and then3.7 80 stacks were connected in apack series. For the measuring circuit, Rin 01 = 2000 KΩ, cells (ICR18650 3.7 V/2.6 Ah)were for the bench test. pack, 20 cells were connected in KΩ, parallel as a stack, and then 80 stacks connected in aWithin series. this For the measuring circuit, R01 = 2000 R02 R02 = 2000 KΩ, Rs = 10 KΩ, and T = 1200 s. The electronic load was provided by AVL e-Storage Tester =as2000 KΩ,and Rs =then 10 KΩ, and Twere = 1200 s. The electronic provided by AVLRe-Storage Tester a stack, 80 stacks connected in a series.load For was the measuring circuit, 01 = 2000 KΩ, R02 (https://www.avl.com/-/avl-e-storage). Theelectronic working conditionshown is shown in Figure 11a. Figure 11b = 2000 KΩ, Rs = 10 KΩ, and T = 1200 s.The Theworking load wasis provided AVL 11a. e-Storage Tester (https://www.avl.com/-/avl-e-storage). condition inby Figure Figure 11b shows the current and voltage of the battery pack. (https://www.avl.com/-/avl-e-storage). The working condition is shown in Figure 11a. Figure 11b shows the current and voltage of the battery pack. shows the current and voltage of the battery pack.
Figure 10. Battery pack and electronic load. Figure 10. Battery pack and electronic load.
Figure 10. Battery pack and electronic load. 150 100 100 50
50 0 0 200 400 600 800 1000 1200 0 Time /s 800 1000 1200 0 (a)Speed 200 400 profile 600 for the experiment Time /s (a)Speed profile for the experiment 400 350 400 300 350 250 300 200 250 200 100 50 100 0 50 -50 -1000 -500 200 400 600 800 1000 1200 -100 Time 0 600/s 800 1200 (b)The 200 voltage400 and current of the1000 battery pack Time /s (b)The voltage and current of the battery pack
Pack volteage Pack volteage /V /V
Current Current /A /A
Speed (Km/h) Speed (Km/h)
150
Figure 11. (a) Work condition; (b) Voltage and current. Figure 11. (a) Work condition; (b) Voltage and current.
Figure 11. (a) Work condition; (b) Voltage and current. In the first group of tests, a 2-MΩ resistor was connected in parallel between the battery pack In the first chassis. group ofAs tests, a 2-MΩ resistor was connected parallel between the battery and the vehicle shown in Figure 12a, although theinmeasured values were affectedpack by In thethefirst group of the tests, a 2-MΩinKalman resistor wasalthough connected parallelvalues between battery and vehicle chassis. As shown Figure filtering 12a, the in measured werethe affected bypack measurement noise, extended algorithm reduced this influence. At the and the vehicleofchassis. As in Kalman Figure although theafter measured values were affected measurement noise, the shown extended filtering algorithm reduced influence. At the by beginning the measurement process, error 12a, quickly converged only athis few iterations. Figure beginning of the measurement process, errormethods. quickly converged onlyinfluence. a few iterations. Figure 12b showsnoise, the measurement errors of the filtering two After kreduced = 5 s,after the error of the extended Kalman measurement the extended Kalman algorithm this At the beginning 12b shows the measurement errors of thetest two methods. Afterthe k =feasibility 5 s,athe error of the extended Kalman algorithm was below 0.5%. The results verified of the proposed model of thefiltering measurement process, error quickly converged after only few iterations. Figure 12bfor shows battery pack monitoring circuit and the effectiveness of the insulation monitoring algorithm based filtering algorithm was below 0.5%. The test results verified the feasibility of the proposed model for the measurement errors of the two methods. After k = 5 s, the error of the extended Kalman filtering battery pack monitoring circuit and the effectiveness the insulation monitoring algorithm based on extended Kalman filtering. algorithm was below 0.5%. The test results verified theoffeasibility of the proposed model for battery on extended Kalman filtering. The key to insulation monitoring is maintaining the accurate measurement of system insulation pack monitoring circuit and the effectiveness of the insulation monitoring algorithm based on extended The key to insulation maintaining the accurate measurement of system insulation insulation resistance under external monitoring interferenceis when the system is suffering from degraded Kalman filtering. resistance under external interference when the system is suffering from degraded insulation
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The key to insulation monitoring is maintaining the accurate measurement of system insulation Energiesunder 2017, 10, external 714 of 13 resistance interference when the system is suffering from degraded11insulation Energies 2017, 10, 714 of 13 performance. Therefore, during the second group of tests, a 20-KΩ resistor was connected11in parallel performance. Therefore, during the second group of tests, a 20-KΩ resistor was connected in parallel between the battery pack system and the vehicle chassis to simulate poor insulation resistance. Insulation Resistance (KΩ)(KΩ) Insulation Resistance
between the battery packduring systemthe and the vehicle poor insulation resistance. performance. Therefore, second groupchassis of tests,toasimulate 20-KΩ resistor was connected in parallel between the battery pack system and the vehicle chassis to simulate poor insulation resistance. 2080
Measured Value EKF Value Measured Value Ideal Value EKF Value Ideal Value
2080 2040 2040 2000 2000 1960
Resistance Errors (%) (%) Resistance Errors
1960
0
200
400
600
800 1000 1200
Time /s
0 (a)Battery 200 400 800 Resistance 1000 1200 Pack600 Insulation Time /s
4
(a)Battery Pack Insulation Resistance Measured Error 4 EKF Error 2 Measured Error EKF Error 2 0 0 -2 -2
0
200
400
600
800 1000 1200
Time /s
0(b)Error 200 Curves 400 of 600 800 Resistance 1000 1200 Insulation Time /s
of Insulation Resistance(with 2 MΩ resistance). (a) Figure 12. Comparison and error (b)Error analysisCurves of insulation resistances Figure 12. Comparison and error analysis of insulation resistances (with 2 MΩ resistance). Comparison of insulation resistances; (b) Error analysis of insulation resistances. Figure 12. of Comparison error analysis of insulation (with 2 MΩ resistance). (a) (a) Comparison insulationand resistances; (b) Error analysis resistances of insulation resistances. Comparison of insulation resistances; (b) Error analysis of insulation resistances.
Figure 13a shows the measurement results of insulation resistance before and after adopting the
Figure 13a showsfiltering the measurement results ofininsulation resistance before and after adopting extended algorithm. As shown Figure resistance 13b, the highest errorafter of the extended FigureKalman 13a shows the measurement results of insulation before and adopting the the extended Kalman filtering algorithm. As shown in Figure 13b, the highest error of the extended Kalman filtering which canAsreach 30%, was generated initial period and extended Kalman algorithm, filtering algorithm. shown in Figure 13b, the during highest the error of the extended Kalman filtering algorithm, can without reach 30%, was generated the initial period and stabilized stabilized within 5%. which However, the30%, algorithm, theduring measurement remained at Kalman filtering algorithm, which can reach was generated during the error initial period and approximately 20%. After calculation, the root mean square error was 8823.66 Ω without the extended withinstabilized 5%. However, without the algorithm, the measurement remained at approximately within 5%. However, without the algorithm, theerror measurement error remained at 20%. Kalman filtering and decreased to 226.35 Ωwas with the extended Kalman the approximately 20%. After calculation, the root mean square error was 8823.66 Ω withoutTherefore, the extended After calculation, the root mean square error 8823.66 Ω without the filtering. extended Kalman filtering extended Kalman filtering algorithm mitigates the majority of the error and improves measurement Kalman filtering and decreased to 226.35 Ω with the extended Kalman filtering. Therefore, the and decreased to 226.35 Ω with the extended Kalman filtering. Therefore, the extended Kalman reliability.Kalman Under filtering the same experimental conditions, theofextended Kalman filtering algorithm extended algorithm the majority the error and improves measurement filtering algorithm mitigates the majoritymitigates of the error and improves measurement reliability. Under the significantlyUnder improves the measurement under while reliability. the same experimentalaccuracy conditions, thedegraded extendedinsulation Kalman performance filtering algorithm same experimental conditions, the extended Kalman filtering algorithm significantly improves the offering satisfactory robustness. significantly improves the measurement accuracy under degraded insulation performance while measurement accuracy under degraded insulation performance while offering satisfactory robustness.
Resistance Errors (%) (%) Resistance Errors
Insulation Resistance (KΩ)(KΩ) Insulation Resistance
offering satisfactory robustness.
31 29 31 27 29 25 27 23 25 21 23 19 21 17 19 15 17 0 15 0 40
Measured Value EKF Value Measured Value Ideal Value EKF Value Ideal Value 200
400
600
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Time /s
200 400 600 800 1000 1200 (a)Battery Pack Insulation Resistance Time /s
(a)Battery Pack Insulation Resistance Measured Error 40 EKF Error 20 Measured Error EKF Error 20 0 0 -20 0 200 400 600 800 1000 1200 -20 Time /s 0(b)Error 200 Curves 400 of 600 800 Resistance 1000 1200 Insulation Time /s
Curves of Insulation Resistance(with 20 KΩ resistance). (a) Figure 13. Comparison and error(b)Error analysis of insulation resistances Comparison of insulationand resistances; (b) Error of insulation Figure 13. Comparison error analysis of analysis insulation resistancesresistances. (with 20 KΩ resistance). (a) Figure 13. Comparison and error analysis of insulation resistances (with 20 KΩ resistance). Comparison of insulation resistances; (b) Error analysis of insulation resistances.
(a) Comparison of insulation resistances; (b) Error analysis of insulation resistances.
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6. Conclusions As seen from the results of the two groups of tests, when the vehicle was operated under complex working conditions, the insulation resistance monitoring circuit exhibited strong performance in mitigating interference regardless of the state of the system’s insulation resistance. Figures 12b and 13b show that the extended Kalman filtering algorithm significantly improves the measurement accuracy while offering satisfactory robustness under degraded insulation performance. After t = 50 s, the error of the extended Kalman filtering algorithm was below 1.5%. However, without the algorithm, the measurement error remained at approximately 20%. Compared with the high-voltage AC signal, the low-voltage AC signal in this paper will not affect the safe use of the battery pack. Although the model has several limitations (for example, this method will slightly increase storage space and computation time), the experimental results show that the insulation monitoring circuit based on the extended Kalman filtering algorithm is effective and significantly improves estimation accuracy and robustness. Acknowledgments: This research is funded by the Key Tackling Item in Science and Technology Department of Jilin Province (Grant No. 20150204017GX) and supported by Graduate Innovation Fund of Jilin University (Project 2016076). Author Contributions: Chuanxue Song and Yulong Shao conceived and designed the experiments; Yulong Shao and Da Wang performed the experiments; Silun Peng analyzed the data; Fang Zhou and Cheng Chang contributed analysis tools; Yulong Shao and Da Wang wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
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