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Study on Factors for Accurate Open Circuit Voltage Characterizations in Mn-Type Li-Ion Batteries Natthawuth Somakettarin * and Tsuyoshi Funaki Division of Electrical, Electronic and Information Engineering, Graduate School of Engineering, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-66-879-7709 Academic Editor: Maciej Swierczynski Received: 1 September 2016; Accepted: 8 March 2017; Published: 12 March 2017

Abstract: Open circuit voltage (OCV) of lithium batteries has been of interest since the battery management system (BMS) requires an accurate knowledge of the voltage characteristics of any Li-ion batteries. This article presents an OCV characteristic for lithium manganese oxide (LMO) batteries under several experimental operating conditions, and discusses factors for accurate OCV determination. A test system is developed for OCV characterization based on the OCV pulse test method. Various factors for the OCV behavior, such as resting period, step-size of the pulse test, testing current amplitude, hysteresis phenomena, and terminal voltage relationship, are investigated and evaluated. To this end, a general OCV model based on state of charge (SOC) tracking is developed and validated with satisfactory results. Keywords: lithium-ion; battery characterization; lithium manganese oxide (LMO); open circuit voltage (OCV); battery test system; battery modeling

1. Introduction Nowadays, Li-ion batteries (LIBs) can be considered as progressive energy storage devices. They have been widely adopted in many applications, such as electric vehicles, renewable energy storage systems, and telecommunication backup and standby systems. These energy systems require enormous batteries, which consist of large amounts of cells to obtain the desired power, energy, rated current, and voltage. The battery management system (BMS) is necessary for the batteries to estimate the state of charge (SOC), monitor the electrical state and the state of health (SOH), protect and control all of the batteries, and maximize the performance during the operations. The understanding of characteristics and behaviors of the batteries is important for the engineers who develop the BMS algorithms. An open circuit voltage (OCV) of LIBs is one of the important elements, which displays the electrode properties in the battery and acts as an equivalent voltage source of the LIBs. In recent years, many researchers had studied and proposed the achievements regarding the usability of the OCV as a function of the SOC in LIB applications such as with the battery modeling, estimations of state parameters, cell capacity, and capacity loss in batteries. A non-linear OCV model with single-variable SOC functions based on a practical and usable capacity was introduced by Chen and Rincon-Mora [1] to apply in the LIB model for predicting battery runtime and electrical performance. This model was validated in good agreement with different step-sizes of the testing current for polymer Li-ion and nickel-metal hydride batteries. Pattipati et al. [2] applied a normalized OCV model to a battery fuel gauge in the BMS application, summarizing that the OCV-SOC curves remain the same regardless of the age or temperature of the battery as long as the actual battery capacity is used in the characterization process. However, Roscher and Sauer [3] proposed applying recovery and hysteresis factors to the OCV function of olivine-type cathode batteries (LiFePO4 or LFP) for the SOC estimation. The empirical OCV model extracted from the experiments can also Batteries 2017, 3, 8; doi:10.3390/batteries3010008

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be applied into a dual extended Kalman filter (DEKF) algorithm in order to estimate the SOC and battery capacity for the online applications by using a concept of normalized capacity computation with the same base cut-off voltage [4]. While the OCVs of different aged cells had shown a similar pattern and given a corresponding hysteresis gap, the cycling capacity loss of LIBs can also be approximated from them. Roscher et al. [5] proposed a residual factor that was extracted from the difference between the experiment and the model of the OCV for detecting the percentage of capacity loss of the aged LFP cells. The benefits of the OCVs are not limited only to the state and parameter estimations, and can also be applied for investigating and studying the electrode properties and phase transformation behaviors of the batteries. As we know, for LIBs, the electrode properties can be identified by measuring the battery voltages under very low-current conditions. Petzl and Danzer [6] demonstrated the advancements in the measurement of the OCV by considering the differential voltage and incremental capacity techniques to study the electrode property and the phase transition of LFP batteries. The abovementioned previous studies allow us to realize the limitations and substantial benefits obtained from the OCV characterization. However, the viewpoints of these studies do not concentrate on the comprehensive factors that affected all accurate OCV determinations. Without the investigation of precise conditions, some of the estimation models can only work correctly in a linear range (20%–80% SOC) [7]. By considering the suitable adjusting parameters (e.g., step-size of pulse tests, resting period of the cell, and testing current), the characterization of OCV can help us to collect OCV information in a precise manner with a minimum testing time, especially in testing conditions under non-linear regions of low and high ranges of the SOC. In order to obtain an accurate battery model, it is necessary to investigate the OCV determination with the implementation of testing-parameter adjustments. This is a delicate task for model-based state estimations in the BMS [8]. In this research, we focus on the factors for a precise OCV characterization under different experimental conditions. Several aspects of the adjusting factors for the OCV are discussed and evaluated such as the different step-sizes of pulse tests, resting periods of the cell, testing current amplitudes (C-rates) of the pulse, and continuous charge-discharge tests, hysteresis phenomena, and terminal voltage relationships. The OCV as a function of SOC calculated with an actual capacity is characterized by using a developed programmable test system. In this study, a commercial rechargeable lithium manganese oxide (LMO) battery was used. The working principle and structure of the LMO were summarized in [9]. The characteristic changes of the OCV depend on the difference in electrochemical potentials of their specific material properties of electrodes and the effective concentration of Lithium during operations. The LMO cell comprises of a positive electrode LiMn2 O4 , which has distinctive features such as high nominal voltage per cell, low internal resistance, moderate to high energy density, high discharge current rupturing, better thermal stability for over-charge, and higher safety than a conventional type such as lithium cobalt oxide (LCO) batteries [10–12]. The negative electrode is made from carbon-based lithiated graphite (LiC6 ), and has a prominent property in high storage capacity due to its flat potential profile [13]. However, the negative graphite electrode has significant influences on the reduction of the potential for full cell operations, OCV patterns, and the usable capacity, especially after cycling due to the loss of active material and the degradation from a dissolution of the solid electrolyte interface (SEI) layer [14,15]. Moreover, a characteristic of the graphite electrode on the OCV pattern is more distinguished, especially when compared with other flat potential cathodes, such as LFP batteries [16]. The aim of this study is to understand nonlinear characteristics of the OCV in the LMO, as well as the factors that affect the accurate OCV characteristics in order to obtain precise OCV information for modeling the battery parameters properly in the BMS application. The remainder of this article is organized as follows: Section 2 describes the OCV determination method for the LMO and its definition. Section 3 shows a developed test system for the precise OCV characterization. In Section 4, we discuss and summarize the study results for the factors that affected the accurate OCV determination. Section 5 introduces a general mathematical equation of the OCV model in a function of the SOC for the BMS implementation and the model validation by comparing

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itcomparing with the experimental data. Finally,data. conclusions future recommended research directions are it with the experimental Finally,and conclusions and future recommended research comparing it with the experimental data. Finally, conclusions and future recommended research given in Section 6. directions are given in Section 6. directions are given in Section 6. 2. 2. Open Open Circuit Circuit Voltage VoltageDetermination Determinationfor forLi-Ion Li-IonBattery Battery 2. Open Circuit Voltage Determination for Li-Ion Battery The in the theelectrical electricalequivalent equivalentcircuit circuitmodel model shown in Figure is extracted The OCV OCV in ofof thethe LIBLIB shown in Figure 1 is 1extracted as a The OCV in the electrical equivalent circuit (VT) model of the LIB shown in Figure 1 is extracted a as a measured voltage at the battery terminals after resting to recover the battery close to toasits measured voltage at the battery terminals (VT) after resting to recover the battery close its measured voltage at the battery terminals (VT) after resting to recover the battery close to its equilibrium equilibrium state state [6]. [6]. In In Figure Figure 2, 2, the the OCVs OCVs are are determined determined as as aa terminal terminal voltage voltage after after relaxing relaxing from from equilibrium state pulse [6]. Incurrents Figure 2,both the OCVs are determined as a terminal voltage after relaxingcalled from the applied short on the discharge and charge operations. This method the applied short pulse currents both on the discharge and charge operations. This method is is called the applied short pulse currents both on the dischargeintermittent and charge operations. This method is called the the OCV OCV pulse pulse test test method method based based on on the the galvanostatic galvanostatic intermittent titration titration technique technique [17]. [17]. the OCV pulse test method based on the galvanostatic intermittent titration technique [17].

Figure 1. 1. Electrical equivalent equivalent circuit model model of the the Li-ion battery battery (LIB). Figure Figure 1. Electrical Electrical equivalent circuit circuit model of of the Li-ion Li-ion battery (LIB). (LIB).

Figure 2. Current and voltage response for pulse tests to extract the open circuit voltage (OCV). Figure 2. 2. Current Current and and voltage voltage response response for for pulse pulse tests tests to to extract extract the theopen opencircuit circuitvoltage voltage(OCV). (OCV). Figure

After a long resting of at least 60 min for our tested LMO to make sure that the cell voltage is After a long resting of at least 60 min for our tested LMO to make sure that the cell voltage is constant closeresting to its equilibrium shownsure in Section battery Afterand a long of at least 60(The minexperimental for our testeddetails LMO are to make that the4.2), cellthe voltage is constant and close to its equilibrium (The experimental details are shown in Section 4.2), the battery current (Iand B) and voltages across the (The effective series resistance (VESR ) and in transient elements (Vtrans) constant close to its equilibrium experimental details are shown Section 4.2), the battery current (IB) and voltages across the effective series resistance (VESR) and transient elements (Vtrans) become(Izero. Then, the VT in Equation (1) canseries be assumed for (V the OCV: current voltages across the effective resistance ) and transient elements (V trans ) B ) and become zero. Then, the VT in Equation (1) can be assumed for theESR OCV: become zero. Then, the VT in Equation (1) assumed VT can = be OCV −V −for Vtransthe OCV: (1) VT = OCV − VESR (1) ESR − Vtrans ESR −=VVESR (2) ESR −I BVtrans (1) VT = OCV ESR = VESR I B (2) From Figure 1, the other parameters will be=ignored such as: (1) effective series resistance (ESR), ESR V /I (2) B ESR such From Figure 1, the other parameters will be ignored as: (1) effective series resistance (ESR), which reflects the resistances of the connecting wires, electrodes, separator and electrolyte; and which reflects the resistances of the connecting wires, electrodes, andseries electrolyte; and From Figure 1, the other parameters will be ignored such as:separator (1) effective resistance (2) transient elements, which reflect the charge-transfer resistance (R1), double-layer capacitance 1 ), double-layer capacitance (2) transient elements, which reflect the charge-transfer resistance (R (ESR), which reflects the resistances of the connecting wires, electrodes, separator and electrolyte; (C1), diffusion process resistance (R2), and its capacitance (C2) because they have no effect on the (C1),(2) diffusion resistance reflect (R2), and charge-transfer its capacitance (C2) because have no effect on the and transientprocess elements, (R1they ), double-layer capacitance OCV. Usually, the OCV iswhich illustrated asthe a function of theresistance SOC in order to compare between the OCV. Usually, the OCV is illustrated as a function of the SOC in order to compare between the (C process resistance (R2 ), the andstudies. its capacitance (C2 )calculation because they haveon no the effect on the 1 ), diffusion different testing conditions during The SOC based coulomb different testing during as thea studies. The SOC calculation on the coulomb OCV. Usually, theconditions OCV is illustrated of the SOC inthe order tobased compare the counting method, is shown in Equation (3),function and is calculated from actual capacity ofbetween the battery. countingtesting method, is shownduring in Equation (3), andThe is calculated from the actual capacity of thecounting battery. different conditions the studies. SOC calculation based on the coulomb In addition, the SOCs between 0% and 100% are set within the operating voltage ranges of the cell In addition, the SOCs between 0% and 100% are set within the operating voltage rangesInofaddition, the cell method, shown Equation (3), and is calculated from the actual capacity of the battery. betweenis3.0 V andin4.2 V, respectively: between 3.0 V and 4.2 V, respectively:

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the SOCs between 0% and 100% are set within the operating voltage ranges of the cell between 3.0 V and 4.2 V, respectively: tcut − off

tcut Z −off SOC (t ) = SOC 0 −



SOC (t) = SOC0 −

t0

t0

IB IB dt 3600 × Q B dt

(3) (3)

3600 × Q B

where IB is the battery current, which is positive for discharging and negative for charging; QB is an where IB is the battery current, which is positive for discharging and negative for charging; QB is an accumulated capacity of the battery in Ah; and SOC0 is an initial value of the SOC. accumulated capacity of the battery in Ah; and SOC0 is an initial value of the SOC. 3. Characterization System System 3. Open Open Circuit Circuit Voltage Voltage Characterization The The OCV OCV characteristics characteristics are are different different and and unique unique depending depending on on their their active active electrode electrode materials materials for the different types of the LIB [18]. It takes a significant amount of time to characterize for the different types of the LIB [18]. It takes a significant amount of time to characterize the the OCV. OCV. In to identify identify the the precise precise OCV OCV characteristics In order order to characteristics based based on on the the sequential sequential pulse pulse tests, tests, aa reliable reliable LIB LIB test system is needed. A manganese-type single cell from NEC-Tokin (Chiyoda, Tokyo, Japan) was test system is needed. A manganese-type single cell from NEC-Tokin (Chiyoda, Tokyo, Japan) was used 1. In In this this section, section, the the developed developed test used in in this this study. study. A A cell cell specification specification is is shown shown in in Table Table 1. test system system with computer-based controlling is introduced for the OCV characterization, as illustrated in Figure with computer-based controlling is introduced for the OCV characterization, as illustrated in Figure 3. 3. The system is developed in the Labview Labview environment The test test system is developed in the environment (Japan (Japan National National Instrument Instrument Inc., Inc., Minato, Minato, Tokyo, Japan) for for controlling controlling the the instruments instruments to to charge charge and and discharge discharge the the LIB LIB via via aa general-purpose general-purpose Tokyo, Japan) interface interface bus bus (GPIB) (GPIB) controller. controller. Table 1. Cell specification. Description Specification Description Specification Electrode/type Spinel single cell Electrode/type Spinel single cell Positive Manganese (LiMn2O4) Positive Manganese (LiMn2 O4 ) Negative Lithiated graphite Negative Lithiated graphite(LiC (LiC66)) Rated capacity (Typical) Rated capacity 3.5 3.5 AhAh (Typical) Voltage V (Nominal) Voltage 3.83.8 V (Nominal)

Description Description Operating voltage Operating voltage Maximum current (C-rate) Maximum current (C-rate) Operating temp. Operating temp. Cell Celldimension dimension Weight Weight

Charging Discharging Discharging 3.0 V 4.2 V 3.0 V 4.2 V 3.5 A (1C) 20.0 A (5.7C) 3.5 A (1C) 20.0 A (5.7C) ◦ 0–40 °C −10–50 0–40 C −10–50 ◦ C °C 82 82 mm × 171 mmmm × 4.7 mm × 171 × mm 4.7 mm 100 g (Maximum) 100 g (Maximum) Charging

Figure for OCV OCV characterization. Figure 3. 3. A A developed developed LIB LIB test test system system with with computer computer based based control control for characterization.

The test system should operate automatically following the sequential programs with a safety The test system should operate automatically following the sequential programs with a safety for the test parameters such as C-rates, pulse durations, rest times, pulse cycles and protective for the test parameters such as C-rates, pulse durations, rest times, pulse cycles and protective setting setting values for operations without malfunctions for any LIB types. The system also records the values for operations without malfunctions for any LIB types. The system also records the related related parameters and status of the LIB during the testing such as battery voltage, current, parameters and status of the LIB during the testing such as battery voltage, current, left-cycle, piecewise left-cycle, piecewise pulse duration, rest duration, date, time, status of testing, and the alarm pulse duration, rest duration, date, time, status of testing, and the alarm message in case of reaching message in case of reaching the protection limits via the display monitor. The sampling interval the protection limits via the display monitor. The sampling interval is set to 10 ms/sampling, which is is set to 10 ms/sampling, which is sufficient to observe the pulse transient response for the precise sufficient to observe the pulse transient response for the precise OCV characterization. OCV characterization. 4. Discussion on the Factors for Accurate Open Circuit Voltage Determination 4. Discussion on the Factors for Accurate Open Circuit Voltage Determination In this section, the effects of the step-sizes and resting periods of the cell during the pulse tests In this section, the effects thepulse step-sizes and restingcharge-discharge periods of the cell during the pulse tests and current amplitudes duringofthe and continuous tests are experimentally and current amplitudes during the pulse and continuous charge-discharge tests are experimentally investigated and discussed for the suitability of testing conditions to provide an accurate OCV characterization by using the developed test system in Section 3.

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investigated and discussed for the suitability of testing conditions to provide an accurate OCV characterization Batteries 2017, 3, 8 by using the developed test system in Section 3. 5 of 13 4.1. 4.1. Effects Effects of of Step-Sizes Step-Sizes during during Pulse Pulse Tests Testson onthe theOpen OpenCircuit CircuitVoltage VoltageCharacteristic Characteristic For OCVs were extracted fromfrom the pulse tests at different step-sizes. Step-sizes (∆SOC) For this thisstudy, study, OCVs were extracted the pulse tests at different step-sizes. Step-sizes ◦ C with 10 min resting) are set at 0.5%, 1%, 5%, and 10% using the same condition (at 1C-rate 20 (ΔSOC) are set at 0.5%, 1%, 5%, and 10% using the same condition (at 1C-rate 20°C with 10 min separately for each pulse charge and discharge. ∆SOC 0.5%, 1%, 5%, and 10%, means the setting resting) separately for each pulse charge and discharge. ΔSOC 0.5%, 1%, 5%,which and 10%, which means of the step-size of the pulse tests was equally at 0.5%, 1%, 5%, and 10%, respectively, between 0% and the setting of the step-size of the pulse tests was equally at 0.5%, 1%, 5%, and 10%, respectively, 100% of the on theΔSOC other1%–5% hand means theother variable pulse between 0%SOC andrange. 100% ∆SOC of the 1%–5% SOC range. on the handstep-size means of thethe variable tests has aof1% fortests the 0%–10% SOC which are in non-linear operating step-size thestep pulse has a 1%and stepthe for90%–100% the 0%–10% andranges, the 90%–100% SOC ranges, which are in regions of the battery, and a 5% step for the 10%–90% SOC range, which is in the linear region. The non-linear operating regions of the battery, and a 5% step for the 10%–90% SOC range, which tests is in were performed within the limits the rated voltage between V and 4.2 V. voltage The effect of step-sizes of the linear region. The tests wereof performed within the limits3 of the rated between 3 V and pulse tests to the OCV characteristic are shown in Figure 4. ∆SOC 1% and 0.5% give the same OCV 4.2 V. The effect of step-sizes of pulse tests to the OCV characteristic are shown in Figure 4. ΔSOC 1% characteristic allsame SOC ranges. ∆SOC 5% also the same OCV result thegives SOC range between and 0.5% giveforthe OCV characteristic forgives all SOC ranges. ΔSOC 5%for also the same OCV 10% However, it gives 10% an inconsistent OCV foritthe SOC belowOCV 10%for and above resultand for 90%. the SOC range between and 90%. However, gives anranges inconsistent the SOC 90% (non-linear regions). During these non-linear regions (windows A and C in Figure 4), the larger ranges below 10% and above 90% (non-linear regions). During these non-linear regions (windows A step-size the OCVprominently pattern. Moreover, wide causeMoreover, the incomplete OCV and C in prominently Figure 4), theaffects largertostep-size affects to thesteps OCV also pattern. wide steps measurement a low SOC OCV rangemeasurement (0%–10%), as illustrated by the blue(0%–10%), and green dots in Window of also cause theinincomplete in a low SOC range as illustrated byBthe Figure 4b. These incomplete and incorrect OCVs resulted from a long pulse release time that caused blue and green dots in Window B of Figure 4b. These incomplete and incorrect OCVs resulted from a the resolution forcaused OCV extraction. longinadequate pulse release time that the inadequate resolution for OCV extraction. In summary, the 1% step-size In summary, the 1% step-size is is sufficient sufficient for for precise precise OCV OCV characterization characterization for for SOC SOC ranges ranges below 10% and above 90%, and the 5% step-size for the 10%–90% SOC range. Figure 4 shows below above 90%, and the 5% step-size for the 10%–90% SOC range. Figure 4 alsoalso shows the the extracted OCVs a step-size ∆SOC1%–5%. 1%–5%.ΔSOC ∆SOC1%–5% 1%–5%also also gives gives aa satisfactory OCV extracted OCVs for for a step-size at atΔSOC OCV characteristic. characteristic. Therefore, Therefore, the the ∆SOC ΔSOC 1%–5% 1%–5% should should be be chosen chosen to to apply apply for for all all of of our our tests. tests.

(a)

(b)

Figure 4.4.Effects Effectsofofstep-sizes step-sizes during pulse on OCV the OCV characteristic 20 °C10with 10 min Figure during pulse teststests on the characteristic at 20 ◦at C with min resting: resting: (a) under the charge test; and (b) under the discharge test. (a) under the charge test; and (b) under the discharge test.

4.2. Effects Effects of of Resting Resting Periods Periods during during Pulse Pulse Tests Testson onthe theOpen OpenCircuit CircuitVoltage VoltageCharacteristic Characteristic 4.2. In order orderto tostudy studythe theeffects effectsofofresting resting periods during pulse tests, voltage of In periods of of thethe cellcell during thethe pulse tests, the the voltage of the the was cell measured was measured forSOC eachstep SOC of the slope percentage of the relaxed voltage cell for each in step termsinofterms the slope percentage of the relaxed voltage (%Slope rv ). (%Slope rv ). The %Sloperv can be calculated with Equation (4). The tests were performed at The %Sloperv can be calculated with Equation (4). The tests were performed at different resting periods different periodsafrom 1 s relaxation to 3 h to identify a suitable relaxation period for the accurate from 1 s toresting 3 h to identify suitable period for the accurate OCV determination: OCV determination:
VSOCi − VSOCi−1 (VSOCi −tVSOCi−1 )
%Sloperv = 100 × (4) % Sloperv = 100 ×tSOCi − SOCi−1 (4) (t − t ) SOCi

SOCi −1

where VSOCi and tSOCi are the voltage and time at the end of the relaxation state for each SOC step, V and are the and time theatstarting where and arevoltage the voltage and at time the endofofthe therelaxation relaxationstate statefor foreach eachSOC SOCstep. step, SOCi−1 V SOCi t SOC i −1 t SOCi VSOCi−1 and t SOCi −1 are the voltage and time at the starting of the relaxation state for each SOC step.

The slopes of the relaxed voltage versus the resting periods illustrated in Figure 5 show that the variation of voltage decayed down near zero after 1 min of resting. The slopes for all SOCs decayed

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The slopes Batteries 2017, 3, 8of the relaxed voltage versus the resting periods illustrated in Figure 5 show that 6 of 13the Batteries 2017, 3, 8 6 of 13 variation of voltage decayed down near zero after 1 min of resting. The slopes for all SOCs decayed down zero min resting.Therefore, Therefore, the the resting resting period period should 1 min down to to zero at at 6060 min ofofresting. shouldbe beevaluated evaluatedbetween between 1 min down to zero at 60 min of resting. Therefore, the resting period should be evaluated between 1 min and 60 min to observe the influence on the extracted OCV. and 60 min to observe the influence on the extracted OCV. and 60 min to observe the influence on the extracted OCV.

Figure5.5.Slopes Slopesof ofthe therelaxed relaxed voltage voltage versus Figure versus the theresting restingperiods. periods. Figure 5. Slopes of the relaxed voltage versus the resting periods.

Figure 6 shows the effect of different resting periods to the extracted OCV under the same Figure 6 shows the1C-rate effect of resting periods to the OCVOCV under same testing Figure 6 shows the effect of with different resting periods to extracted the extracted under the same testing condition (at 20different °C ΔSOC 1%–5%). The low resting period gives athe bloated OCV ◦ C with ∆SOC 1%–5%). The low resting period gives a bloated OCV between condition (at 1C-rate 20 testing condition 1C-rate °Ccannot with ΔSOC The lowcharacteristic resting period gives bloated between 60% and(at 80% SOCs,20 and reflect1%–5%). the actual OCV both on athe chargeOCV and 60% and 80% SOCs, and From cannot reflect the reflect actuala the OCV characteristic both on the charge discharge between 60% and 80% SOCs, and cannot actual OCV characteristic both on theand charge and discharge operations. the experiments, recommended resting period for accurate OCV for operations. From a recommended resting period accurate for this itOCV cell type discharge operations. experiments, recommended resting period OCV for accurate for this cell type isthe at experiments, 60 From min tothe ensure that the acell has reached itsfor equilibrium. However, can be is at 60 min to ensure that the cell has reached its equilibrium. However, it can be reduced to 30 min or this cell type is at 60 min to ensure that the cell has reached its equilibrium. However, it can be reduced to 30 min or 10 min for a fast OCV approximation. 10 reduced min for atofast OCVorapproximation. 30 min 10 min for a fast OCV approximation.

Figure 6. Effects of resting periods on the OCV characteristic. Figure6.6.Effects Effectsof ofresting resting periods periods on Figure on the the OCV OCVcharacteristic. characteristic.

4.3. Effects of Current Amplitudes during Pulse Tests on the Open Circuit Voltage Characteristic 4.3. Effects of Current Amplitudes during Pulse Tests on the Open Circuit Voltage Characteristic 4.3. Effects of Current Amplitudes Tests on the Open (C-rates) Circuit Voltage In order to investigate theduring effectsPulse of current amplitudes on theCharacteristic OCV, the pulse charge In order to investigate the effects of current amplitudes (C-rates) on the OCV, theΔSOC pulse 1%–5% charge and discharge tests were performed under the same testing condition (at 20 °C with In order to investigate the effects of current amplitudes (C-rates) on the OCV, the pulse charge and discharge tests for were performed under thewere sameextracted testing condition (at 20 °C with ΔSOCC/4 1%–5% 60 min resting each pulse). The OCVs for different C-rates between and and discharge tests were performed under the same testing condition (at 20 ◦ C with ∆SOC 1%–5% and and 60 min resting forpulse eachC-rates pulse). on The OCVs extracted for different C-rates between C/4 and 1C. The effects of the the OCVwere are shown in Figure 7. 60 1C. minThe resting forofeach pulse). The OCVs were extracted forFigure different C-rates between C/4 and 1C. pulse C-rates on an theadequate OCV are relaxing shown inperiod 7. that the voltage patterns for Theeffects extractedthe OCV results under show Thethe effects of the pulse C-rates on the OCV are shown in Figure 7. The extracted OCV results under an adequate relaxing period show the voltage patterns for different C-rates correspond to both charge and discharge tests. In that addition, the ESRs are also the different C-rates correspond to both charge and discharge tests. In addition, the ESRs are also extracted from an instantaneous response of the pulse charge and discharge tests. The ESRs are extracted from an response of the pulse charge 8.and discharge tests. The are almost constant forinstantaneous the SOC and C-rates as illustrated in Figure It can be concluded that ESRs the pulse almost for the SOC and C-rates illustrated Figure 8. It can be concluded the pulse currentconstant amplitudes have no effect on the as OCV and ESRincharacteristics under a constantthat temperature current haveperiod. no effect on the9 OCV andthe ESR characteristics under a constant temperature and theamplitudes same resting Figure shows OCV comparison between charge (chg) and and the same period. Figure 9 shows the OCV comparison between acharge and discharge (dis) resting under the different C-rates. During the charge and discharge, small (chg) hysteresis discharge (dis) under the different C-rates. During the charge and discharge, a small hysteresis occurs in the range of 5%–40% SOC, which is magnified in Figure 10. occurs in the range of 5%–40% SOC, which is magnified in Figure 10.

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(a)

(b)

Figure 7. Effects of pulse current amplitudes on the OCV characteristic at 20 °C with 60 min resting:

Figure 7. Effects of pulse current amplitudes on the OCV characteristic at 20 ◦ C with 60 min resting: (a) under the charge test; and (b) under the discharge test. (a) under the charge test; and (b) under the discharge test.

The extracted OCV results under an adequate relaxing period show that the voltage patterns for the different C-rates correspond to both charge and discharge tests. In addition, the ESRs are also extracted from an instantaneous response of the pulse charge and discharge tests. The ESRs are almost constant for the SOC and C-rates as illustrated in Figure 8. It can be concluded that the pulse current amplitudes have no effect on the OCV and ESR characteristics under a constant temperature and the (a) (b) (a) 9 shows the OCV comparison between charge (b) (chg) and discharge (dis) same resting period. Figure 7. Effects of pulse current amplitudes OCV athysteresis 20 °C °Cwith with60 60min minresting: resting: under Figure theFigure different C-rates. During the chargeon and discharge, a smallat occurs in the range of 7. Effects of pulse current amplitudes onthe the OCV characteristic characteristic 20 (a) SOC, under the charge test; and (b) under the discharge test. 5%–40% which is magnified in Figure 10. (a) under the charge test; and (b) under the discharge test.

Figure 8. Effects of pulse current amplitudes on the effective series resistance (ESR) characteristic tested at 20 °C with 60 min resting.

Figure 8. Effects of pulse current amplitudes on the effective series resistance (ESR) characteristic Figure 8. 8. Effects of of pulse current amplitudes on on thethe effective series resistance (ESR) characteristic tested Figure Effects pulse current amplitudes effective series resistance (ESR) characteristic tested at 20 °C with 60 min resting. ◦ attested 20 C at with 60 with min 60 resting. 20 °C min resting.

Figure 9. Hysteresis occurrence on the OCV characteristics tested at 20 °C with 60 min resting.

Figure 10 shows that the C-rates of the pulse tests also have no effect on the hysteresis character. The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects and microscopic distortions within the active electrode material during Li-intercalation, is unique for each cell material [19]. This cell type illustrates a narrow hysteresis property between the charge and discharge. The difference in OCV (ΔOCV) for the charge and discharge to the averaged values is shown in Figure 11. The maximum and minimum voltage gaps of the averaged OCV that occurred at 25% SOC are only ±14.368 mV, or ±0.379% of its average value. Figure 9. Hysteresis occurrence on the OCV characteristics tested at 20 °C with 60 min resting.

Figure9.9.Hysteresis Hysteresisoccurrence occurrence on on the the OCV characteristics tested atat2020 °C◦ C with 60 60 min resting. Figure OCV characteristics tested with min resting. Figure 10 shows that the C-rates of the pulse tests also have no effect on the hysteresis character. The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects and Figure 10 shows that the C-rates of the pulse tests also have no effect on the hysteresis character. microscopic distortions within the active electrode material during Li-intercalation, is unique for The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects and each cell material [19]. This cell type illustrates a narrow hysteresis property between the charge microscopic distortions within the active electrode material during Li-intercalation, is unique for and discharge. each cellThe material [19].inThis typefor illustrates a narrow hysteresis charge difference OCVcell (ΔOCV) the charge and discharge to theproperty averagedbetween values is the shown in andFigure discharge. 11. The maximum and minimum voltage gaps of the averaged OCV that occurred at 25% SOC

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Figure 10. Zoom of the hysteresis occurrence tested at 20 °C Figure 10. Zoom of the hysteresis occurrence tested at 20 ◦ Cwith with6060min minresting. resting.

Figure 10 shows that the C-rates of the pulse tests also have no effect on the hysteresis character. The hysteresis, which results from mechanical stress, thermo-dynamical entropic effects and microscopic distortions within the active electrode material during Li-intercalation, is unique for each cell material [19]. This cell type illustrates a narrow hysteresis property between the charge and discharge. The difference in OCV (∆OCV) for the charge and discharge to the averaged values is shown in Figure 11. The maximum and minimum voltage gaps of the averaged OCV that occurred at 25% SOC are only ±14.368 mV,10. orZoom ±0.379% its average value. tested at 20 °C with 60 min resting. Figure of theofhysteresis occurrence

Figure 11. ΔOCV for the averaged charge and discharge values tested at 20 °C with 60 min resting.

4.4. Effects of Current Amplitudes during Continuous Charge and Discharge Tests on the Open Circuit Voltage Approximation In this study, continuous charge and discharge tests were performed with different current amplitudes (C-rates) between C/40 and 1C within the operating voltage ranges of the cell in order to study the influence of C-rates on the terminal voltage characteristics (VTs), and then to investigate the relationship of VTs on the OCV approximation. The effects of different C-rates on the terminal voltage characteristic are shown in Figure 12. The C-rates lower than C/20 do not obviously show the characteristic difference. However, the lower C-rates clearly illustrate the appearance of curly trends on both charge and discharge voltage profiles, especially between 60% and 80% SOCs as shown in Figure 11. 11. ∆OCV ΔOCV for the averaged averaged charge charge and and discharge discharge values values tested tested at at 20 20 ◦°C with 60 60 min min resting. resting. Figure for the C with Figure 12a,b, respectively. Figure 13 shows the relationship between the average OCV and charge/discharge terminal 4.4. Effects of Current Amplitudes during Continuous Charge and Discharge Tests on the Open Circuit 4.4.voltages Effects ofunder Current Amplitudes during Continuous Charge andVTs Discharge on the Open Circuit different C-rates. Figure 13a shows that the for lowTests C-rates precisely illustrate Voltage Approximation Approximation Voltage the OCV. The polarization voltage gaps between charge and discharge VTs at the same C-rate can be reduced the low C-rate. The polarization mechanism the VTs is directly influenced the In this thisfor study, continuous charge and discharge discharge testsofwere were performed with differentby current In study, continuous charge and tests performed with different current C-rate. The(C-rates) cell operating at the higher current presents more polarization effects. of Asthe aforementioned amplitudes between C/40 and 1C within the operating voltage ranges cell in order to amplitudes (C-rates) between C/40 and 1C within the operating voltage ranges of the cell in order in Section 4.3, the ESRs and OCVs for each charging and discharging do not change for the C-rates. study thethe influence ofofC-rates to investigate investigate to study influence C-ratesononthe theterminal terminalvoltage voltagecharacteristics characteristics(VTs), (VTs), and and then then to Therefore, the voltage drops across the ESR depend on theeffects current, resulting in the increment of the the relationship of VTs on the OCV approximation. The of different C-rates on the terminal the relationship of VTs on the OCV approximation. The effects of different C-rates on the terminal terminal voltage. It are canshown be recommended that the OCVlower characteristic be approximated bythe voltage characteristic inFigure Figure12. 12.The TheC-rates C-rates thanC/20 C/20can do not not obviously show show voltage characteristic are shown in lower than do obviously the measuring a terminal voltage at the low testing current. characteristic difference. However, the lower C-rates clearly illustrate the appearance of curly trends characteristic However, C-rates clearly appearance of curly trends Figure difference. 13b shows the mean ofthe thelower squared residuals of illustrate the errorsthe (MSE C-rate) between the OCV on both both charge charge and and discharge discharge voltage voltage profiles, profiles, especially especially between between 60% 60% and and 80% 80% SOCs SOCs as as shown shown in in on and terminal voltage for each C-rate of Figure 13a, and shows a testing time reduction for the OCV Figure 12a,b, 12a,b, respectively. respectively. Figure approximation under different rates of continuous testing current.

Figure 13 shows the relationship between the average OCV and charge/discharge terminal voltages under different C-rates. Figure 13a shows that the VTs for low C-rates precisely illustrate the OCV. The polarization voltage gaps between charge and discharge VTs at the same C-rate can be reduced for the low C-rate. The polarization mechanism of the VTs is directly influenced by the C-rate. The cell operating at the higher current presents more polarization effects. As aforementioned in Section 4.3, the ESRs and OCVs for each charging and discharging do not change for the C-rates. Therefore, the voltage drops across the ESR depend on the current, resulting in the increment of the

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(a)

(b)

Figure 12. Effects of current amplitudes on the terminal voltage characteristic at 20 °C: (a) under Figure 12. Effects of current amplitudes on the terminal voltage characteristic at 20 ◦ C: (a) under continuous Batteries 2017, 3, 8 charging; and (b) under continuous discharging. 9 of 13 continuous charging; and (b) under continuous discharging.

Figure 13 shows the relationship between the average OCV and charge/discharge terminal voltages under different C-rates. Figure 13a shows that the VTs for low C-rates precisely illustrate the OCV. The polarization voltage gaps between charge and discharge VTs at the same C-rate can be reduced for the low C-rate. The polarization mechanism of the VTs is directly influenced by the C-rate. The cell operating at the higher current presents more polarization effects. As aforementioned in Section 4.3, the ESRs and OCVs for each charging and discharging do not change for the C-rates. Therefore, the voltage drops across the ESR depend on the current, resulting in the increment of the terminal voltage. It can be recommended that the OCV characteristic can be approximated by measuring a terminal voltage at the low testing current. (a) (b) (b) Figure 13b shows the mean of the squared residuals of the errors (MSE C-rate ) between the OCV Figure 12. 13. Effects Terminal voltage relationship to the OCV approximation: (a) polarization differences of OCV and terminal voltage for C-rate of Figure 13a, and shows testing timeatreduction for the Figure of each current amplitudes on the terminal voltageacharacteristic 20 °C: (a) under terminal voltages under different rates of continuous testing current on the average OCV; (b) mean of continuous charging; and (b)rates under discharging. approximation under different ofcontinuous continuous testing current. the squared residuals of the errors (MSE) and testing time reduction for OCV approximation under different rates of continuous testing current.

The MSEC-rate can be determined separately for charge and discharge by using Equation (5): SOC

MSEC−rate =

(

2

)

n 1 VTSOCi − OCV (SOCi ) n SOC

(5)

i =1

where VTSOCi is a measured terminal voltage at SOCi for a continuous test, OCV(SOC)i is an open circuit voltage obtained by OCV averaging at the different C-rates as a function of SOCi for a sampling number n separately for charge and discharge. A recommended (a) continuous testing current rate for the OCV approximation is C/20 because it (b) can save time for charge and discharge tests from 82.86 h to 40.71 h (or 50.87%) with low MSEs of Figure 13. Terminal voltage relationship to the OCV approximation: (a) polarization differences of Figure 13. ×Terminal voltage relationship approximation: (a) respectively. polarization differences only 0.1284 10−3 V2 and 0.0771 × 10−3 V2 to forthe theOCV charge and discharge, Moreover,ofit is terminal voltages under different rates of continuous testing current on the average OCV; (b) mean of terminal voltages under different rates of continuous testing current on the average OCV; mean −3 V2 of also the faster than the C/40 rate by 52.39% with the difference of MSEs of only 0.0197 (b) × 10 and squared residuals of the errors (MSE) and testing time reduction for OCV approximation under the squared residuals of the errors (MSE) and testing time reduction for OCV approximation under −3 2 0.0263 × 10 V for the charge and discharge, respectively. different rates of continuous testing current. different rates of continuous testing current.

5. Open Modeling separately for charge and discharge by using Equation (5): The Circuit MSEC-rateVoltage can be determined The MSE can be determined separatelyisfor charge and discharge by using Equation (5): C-rate A model of the OCV characteristic in LIBsSOC essential for the BMS 2 in order to estimate the state n 1 of the batteries have been proposed [2,20]. They are variables during operations. Many OCV models MSE VTSOCi − OCV (SOCi ) (5) 2 C−rate =SOC n n SOC
1 related to the internal chemical variation of the batteries to fit with the tested results, depending on(5) i =1 MSEC−rate = VTSOCi − OCV (SOCi ) ∑ The n SOC the purpose of the study and their applications. factors that affected the OCV pattern are studied 1 SOCi for a continuous test, OCV(SOC)i is an open where VTSOCi is a measured terminal voltagei=at in Section 4, and the step-size of the pulse test and resting period are adjusted to obtain the accurate i an foropen a circuit voltage byalso OCV averaging the different C-rates as test, a function of no SOC where aobtained measured terminal voltage at SOC for testing a continuous OCV(SOC) OCV.VT At thei is same time, we found that theat rates of current (C-rates) have effect on SOC i the i is sampling number n separately for charge and discharge. circuit voltage obtained by OCV averaging at the different C-rates as a function of SOC for a sampling the OCV. The representative of a precise OCV from the experiments under these conditions can be i current rate for the OCV approximation is C/20 because it numberAnrecommended separately forcontinuous charge andtesting discharge. can save time for charge and discharge tests from 82.86 h to 40.71 h (or 50.87%) with low MSEs of only 0.1284 × 10−3 V2 and 0.0771 × 10−3 V2 for the charge and discharge, respectively. Moreover, it is also faster than the C/40 rate by 52.39% with the difference of MSEs of only 0.0197 × 10−3 V2 and 0.0263 × 10−3 V2 for the charge and discharge, respectively.

(

5. Open Circuit Voltage Modeling

)

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A recommended continuous testing current rate for the OCV approximation is C/20 because it can save time for charge and discharge tests from 82.86 h to 40.71 h (or 50.87%) with low MSEs of only 0.1284 × 10−3 V2 and 0.0771 × 10−3 V2 for the charge and discharge, respectively. Moreover, it is also faster than the C/40 rate by 52.39% with the difference of MSEs of only 0.0197 × 10−3 V2 and 0.0263 × 10−3 V2 for the charge and discharge, respectively. 5. Open Circuit Voltage Modeling A model of the OCV characteristic in LIBs is essential for the BMS in order to estimate the state variables during operations. Many OCV models of the batteries have been proposed [2,20]. They are related to the internal chemical variation of the batteries to fit with the tested results, depending on the purpose of the study and their applications. The factors that affected the OCV pattern are studied in Section 4, and the step-size of the pulse test and resting period are adjusted to obtain the accurate OCV. At the same time, we also found that the rates of the testing current (C-rates) have no effect on the OCV. The representative of a precise OCV from the experiments under these conditions can be obtained by averaging the simplified Batteries 2017, 3, 8OCV under C-rates separately for the charge and discharge. Therefore, a 10 of 13 OCV model for the LMO can only be developed as a function of SOC, and then it is validated with the obtained by averaging the OCV under high-order C-rates separately for the is charge Therefore, a experimental OCV data. The empirical polynomial usedand fordischarge. implementing the model simplified OCV model for the LMO can only be developed as a function of SOC, and then it is with a real-time calculation in the BMS application, as shown in Equation (6): validated with the experimental OCV data. The empirical high-order polynomial is used for  BMS application, as shown in n  in the implementing the model with a real-time calculation OCV (SOC ) = ∑ k j SOC j Equation (6):

(6)

j=0 n

SOC ) (6)  (kwith The coefficients (kj ) in Equation (6) are determined MATLAB (MathWorks Japan, Nagoya, OCV ( SOC ) =

j

j

j=0

Aichi, Japan) for the experimental SOC and OCV data from the previous section by using a non-linear The coefficients (kj) in Equation (6) are determined with MATLAB (MathWorks Japan, Nagoya, least Aichi, squareJapan) estimation technique. The objective function is given, as in Equation (7): for the experimental SOC and OCV data from the previous section by using a non-linear least square estimation technique. The objective m function is given, as in Equation (7): 2 min k f (k, SOC ) − OCV k2 = min ∑ m [ f ( k, SOCi ) − OCVi ]

min f (k , SOC ) − OCV

k

2

k

(7)



k i = 1[ f (k , SOC ) − OCV ] 2 = min i i k

(7)

i =1

where k is the SOC coefficient to be optimized; j is the degree of polynomial; n is the highest-order of where k is the SOC coefficient to be optimized; j is the degree of polynomial; n is the highest-order of polynomial; and m is the length of SOC and OCV data. polynomial; and m is the length of SOC and OCV data. FromFrom Equation (6), the highest-order (n) for smooth fitting of the OCV analytic function for this Equation (6), the highest-order (n) for smooth fitting of the OCV analytic function for this LMOLMO is 17th for both charging and thisorder, order,the theMSEs MSEs the maximum is 17th for both charging anddischarging. discharging. For For this areare lessless thanthan the maximum − 5 2 criteria (≤1 (≤1 × 10 isprecise preciseenough enough fitting model. The extracted OCV are models that is forfor fitting the the OCVOCV model. The extracted OCV models criteria × 10−5VV2)) that are shown lineininFigure Figure shownby by the the solid solid line 14.14.

(a)

(b)

Figure 14. OCV fitting results for the lithium manganese oxide (LMO) at 20 °C:◦(a) fitting result for Figure 14. OCV fitting results for the lithium manganese oxide (LMO) at 20 C: (a) fitting result for charging; and (b) fitting result for discharging. charging; and (b) fitting result for discharging.

The fitting results from Figure 14 show that the proposed OCV model can illustrate the voltage

The fitting results from Figure 14 show the proposed model can illustrate the voltage characteristics correctly along the SOC rangethat on both charge andOCV discharge operations separately by the hysteresis phenomena. A SOC comparison of both the MSEs of estimation at separately different by characteristics correctly along the range on chargeand anderrors discharge operations polynomial orders for OCV model fitting is shown in Figure 15. The optimum SOC coefficients of the OCV model for charge and discharge are shown in Table 2. Table 2. Optimum state of charge (SOC) coefficients of the OCV model for charge and discharge. SOC Coefficient

Charge

Discharge

SOC Coefficient

Charge

Discharge

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the hysteresis phenomena. A comparison of the MSEs and errors of estimation at different polynomial orders for OCV model fitting is shown in Figure 15. The optimum SOC coefficients of the OCV model forBatteries charge2017, and3, discharge are shown in Table 2. 8 11 of 13

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(a)

(b)

Figure 15. Comparison results of MSEs and errors of estimation at different polynomial orders: Figure 15. Comparison results of MSEs and errors of estimation at different polynomial orders: (a) (a) results for charge; and (b) results for discharge. results for charge; and (b) results for discharge.

The errors of OCV model are evaluated in Figure 16 by MSE). The MSEs for charging and Table 2. Optimum state of charge (SOC) coefficients of the OCV model for charge and discharge. discharging are only 0.7414 × 10−5 V2 and 0.3848 × 10−5 V2, respectively. The minimum, maximum, and average values of SOC the estimation error forCharge charge are −4.7265 × 10−3 V, SOC Coefficient Charge Discharge Coefficient Discharge −3 −8 6.9326 × 10 V, and 7.8056 × 10 V (or −0.1437%, 0.1961%, and 0.00008%), respectively, while the k0 3.0037 3.0016 k9 1.0595 × 10−9 8.4261 × 10−10 −3 −11 (a) (b) minimum, maximum, and average values of the estimation error for discharge are −3.0394 × 10 − 1 − 1 − 11 k1 k10 2.3163 × 10 2.0082 × 10 −2.2638 × 10 −1.8003 × 10V, − 2 −7 V − 6.3308 1.1389 ×results 10 (or −0.0931%, 0.1802%, 0.00004%), respectively. k2 × 10−3 V, and kand −6.5271 × 10 5.0440 ×and 10−2errors 3.6337 × polynomial 10−13 2.8847 × 10−13 11 Figure 15. Comparison of MSEs of estimation at different orders: k3 1.4950 × 10−2 1.1287 × 10−2 (a) and for discharge. 3 results k results for−charge; 2.3529 × 10−(b) −1.7962 × 10−3

k12 −4.3564 × 10−15 k 3.8402 × 10−17 4 13 k5 k14 2.5025 × 10−4 1.9382 × 10−4 −2.4147 × 10−19 k6 −1.8436 10−5 are −1.4444 × 10−5in Figure k16 10−21 for The errors of OCV×model evaluated The ×MSEs 15 by MSE).1.0246 − 7 − 7 k7 k16 9.6864 × 10 × 10−5 V7.6498 10 −2.6280 × 10−24 2 and × discharging are only 0.7414 0.3848 × 10−5 V2, respectively. k8 k17 −3.7174 × 10−8 −2.9500 × 10−8 3.0772 × 10−27

−3.4474 × 10−15 3.0257 × 10−17 −1.8926 × 10−19 −22 7.9827 × 10and charging −2.0344 × 10−24 2.3659 × 10−27 −3

The minimum, maximum, and average values of the estimation error for charge are −4.7265 × 10 V, 6.9326 × 10−3 V, and 7.8056 × 10−8 V (or −0.1437%, 0.1961%, and 0.00008%), respectively, while the The errors of OCV and model are evaluated in estimation Figure 16 error by MSE). The MSEs for charging and minimum, maximum, average values of the for discharge are −3.0394 × 10−3 V, 5 V2 and 0.3848 × 10−5 V2 , respectively. −3 V, discharging only 10−7−V 6.3308 × 10are and0.7414 1.1389 × × 10 (or −0.0931%, 0.1802%, and 0.00004%), respectively.

(a)

(b)

Figure 16. Error evaluation for the OCV model validation for the LMO at 20 °C: (a) error of estimation for charge; and (b) error of estimation for discharge.

6. Conclusions This article studied the factors for the accurate OCV characterization of manganese-type Li-ion batteries for the BMS application. The charge and discharge test system is developed for use with the OCV pulse test method. An automatic battery test system is proposed for OCV characterization. (a) (b) From this study, we found that the accurate OCV for LMO can be obtained with a small step-size evaluation for the OCV model10% validation for the LMO at 20 °C: (a) error the of estimation pulseFigure of 1%16. forError the non-linear regions below and above 90% SOCs. However, step-size can Figure 16. Error evaluation for the OCV model validation for the LMO at 20 ◦ C: (a) error of estimation for charge; and (b) error of estimation for discharge. be increased up to 5% in the range of 10%–90% SOC for faster extraction with a small error. The for charge; and (b) error of estimation for discharge. short resting period of the pulse test directly affects the error of the OCV pattern. A recommended 6. Conclusions resting period for accurate OCV on this battery type is 60 min. The testing current rates (C-rate) of The minimum, maximum, and OCV average values of the estimationcell error for charge are the pulse tests have no the effect to the and ESROCV patterns. This studied illustrates a Li-ion small This article studied factors for the accurate characterization of manganese-type − 3 − 3 − 8 −4.7265 × 10effect V, between 6.9326 ×charge 10 V, and 7.8056 × 10 V with (or −the 0.1437%, 0.1961%, and hysteresis maximum voltage gap0.00008%), of only batteries for the BMS application. and The discharge charge andoperations discharge test system is developed for use with the respectively, while the minimum, maximum, and average values of the estimation 28.736 mV. For relationship of VTs tobattery OCV, the measuring of terminalfor voltage of the cellerror underfor OCV pulse test the method. An automatic test system is proposed OCV characterization. −3 V, 6.3308 × 10−3 V, and 1.1389 × 10−7 V (or −0.0931%, 0.1802%, discharge arestudy, −3.0394 × 10illustrate the low C-rate of C/20 can approximate characteristic with acceptable MSE value From this we found that the the accurate OCV forOCV LMO can be obtained with a small step-size and 0.00004%), respectively. by using only half the time for testing. This article also developed an OCV model for the LMO a pulse of 1% for the non-linear regions below 10% and above 90% SOCs. However, the step-sizeas can polynomial SOC to simplify SOC the numerical calculations in error. the BMS be increased function up to 5%ofin the the range of 10%–90% for faster extraction withusing a small The application. model is validated the affects OCV experimental hasAthe MSE values short restingThe period of the pulse testwith directly the error of results, the OCVwhich pattern. recommended resting period for accurate OCV on this battery type is 60 min. The testing current rates (C-rate) of the pulse tests have no effect to the OCV and ESR patterns. This studied cell illustrates a small hysteresis effect between charge and discharge operations with the maximum voltage gap of only

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6. Conclusions This article studied the factors for the accurate OCV characterization of manganese-type Li-ion batteries for the BMS application. The charge and discharge test system is developed for use with the OCV pulse test method. An automatic battery test system is proposed for OCV characterization. From this study, we found that the accurate OCV for LMO can be obtained with a small step-size pulse of 1% for the non-linear regions below 10% and above 90% SOCs. However, the step-size can be increased up to 5% in the range of 10%–90% SOC for faster extraction with a small error. The short resting period of the pulse test directly affects the error of the OCV pattern. A recommended resting period for accurate OCV on this battery type is 60 min. The testing current rates (C-rate) of the pulse tests have no effect to the OCV and ESR patterns. This studied cell illustrates a small hysteresis effect between charge and discharge operations with the maximum voltage gap of only 28.736 mV. For the relationship of VTs to OCV, the measuring of terminal voltage of the cell under the low C-rate of C/20 can illustrate the approximate OCV characteristic with acceptable MSE value by using only half the time for testing. This article also developed an OCV model for the LMO as a polynomial function of the SOC to simplify the numerical calculations using in the BMS application. The model is validated with the OCV experimental results, which has the MSE values of only 0.7414 × 10−5 V2 and 0.3848 × 10−5 V2 , and the maximum errors are only 0.1961% and 0.1802% for charging and discharging, respectively. However, the OCV characterization and modeling, depending on the temperatures and operating cycles, are still challenging in practical applications. Studies on the changes of the OCV characteristics and their behaviors with the consideration of life cycles and temperatures should be investigated next, and are our next steps in the near future. Acknowledgments: The authors thank the anonymous reviewers for providing useful suggestions and valuable comments that resulted in the improved quality of the paper. Author Contributions: Natthawuth Somakettarin and Tsuyoshi Funaki conceived and designed the experiments; Natthawuth Somakettarin performed the experiments and analyzed the data; Natthawuth Somakettarin and Tsuyoshi Funaki wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

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