Development of an Intelligent Charger with a Battery Diagnosis Function Using Online Impedance Spectroscopy

Abstract

Battery diagnosis is vital to battery-based applications because it ensures system reliability by avoiding battery failure. This paper presents a novel intelligent battery charger with an online diagnosis function to circumvent interruptions in system operation. The charger operates in normal charging and diagnosing modes. The diagnosis function is performed with the impedance spectroscopy technique, which is achieved by injecting a sinusoidal voltage excitation signal to the battery terminals without the need for additional hardware. The impedance spectrum of the battery is calculated based on voltage excitation and current response with the aid of an embedded digital lock in amplifier in a digital signal processor. The measured impedance data are utilized in the application of the complex nonlinear least squares method to extract the battery parameters of the equivalent circuit. These parameters are then compared with the reference values to reach a diagnosis. A prototype of the proposed charger is applied to four valve-regulated lead-acid batteries to measure AC impedance. The results are discussed.

I. INTRODUCTION

Lead–acid batteries are popularly adopted as an energy storage element in battery-based applications because of their reliability and affordability [1]-[7]. Battery performance affects the product’s reliability and lifetime. Thus, the state of health (SOH) of batteries should be assessed to avoid possible replacement costs caused by sudden system failures. Battery SOH during regular usage also provides information on maintenance scheduling and replacement. However, batteries are chemical energy storage devices that deteriorate over time and eventually reach their end of life. Thus, determining an appropriate replacement time is difficult. Battery SOH must be extensively investigated to improve system reliability.

Battery SOH is defined as the relative ratio of the battery capacity at its current state to the nominal capacity when it was new [8], [9]. Previous research has determined that battery SOH is strongly dependent on several factors, such as depth of discharge, temperature variations, and rate of charge/discharge current [10], [11]. The estimation of battery SOH is complex because of the nonlinear relationship between battery SOH and the aforementioned factors. Various methods to estimate SOH have been proposed [12], [13]. An example is the coulomb counting method that estimates battery SOH by counting the maximum available charge of the battery [12]. However, this method cannot be applied during operation because the battery needs to be fully charged and discharged for coulomb counting. Another method is the extended Kalman filter that performs online estimation of the state of charge (SOC) and SOH [13]. This method facilitates the accurate estimation of SOH. However, such method requires a complex estimation algorithm and an accurate model of the battery to obtain reliable results. In addition, estimation accuracy decreases as the battery degrades because the parameters of the equivalent circuit model of the battery vary according to the age of the battery.

Recent research has indicated that battery impedance variation can be a useful tool to investigate battery aging [13], [14]. Several commercially available battery testers diagnose battery aging by measuring the AC impedance of batteries at a frequency of 1 kHz on the basis of the fact that the real part of the complex impedance of a battery at 1 kHz is almost equal to its ohmic resistance [15], [16]. However, the method may lead to inaccurate internal resistance calculations because ohmic resistance does not always match the real part of the impedance at 1 kHz; this inaccuracy may lead to inaccurate internal resistance calculations, which affect aging estimation. In addition, given that battery SOH must be evaluated periodically, such methods are labor intensive and time consuming, particularly for large battery systems.

If the battery diagnosis function can be integrated into the charger, then the reliability of the system can be improved significantly because battery SOH can be periodically monitored [17], [18]. In addition, the cost associated with the maintenance can be greatly reduced if the battery SOH is monitored automatically and regularly.

Recently, in [19], a novel intelligent charger with an embedded diagnosis function was proposed. With the proposed charger, the standard constant current/constant voltage (CC/CV) method was applied in the current study to charge a lead–acid battery in the normal charge mode, and impedance spectroscopy (EIS) was performed with the sinusoidal voltage excitation generated by the voltage controller in the diagnosis mode. The measured current and voltage were used to calculate the impedance spectrum of the battery by using a digital lock-in amplifier (DLIA). With a complex nonlinear least squares fitting method, the parameters for the equivalent circuit of the lead–acid battery were obtained. Comparison of these parameters with those of a fresh lead–acid battery indicated that battery SOH can be estimated. The proposed method can be implemented in any type of bidirectional charge converter without any extra hardware. As a result, the proposed method requires no additional costs.

 

II. SOH OF A LEAD–ACID BATTERY BY USING EIS AND ITS EQUIVALENT CIRCUIT MODEL

A. Electrochemical Impedance Measurement Method

The electrochemical impedance of a battery is a complex quantity that represents the battery’s current state [20]-[24]. It is an effective modeling and diagnosis tool for electrochemical power sources, such as batteries, fuel cells, and supercapacitors. In [20], various methods to measure the electrochemical impedance of batteries were presented. However, most commercially available EIS instruments are expensive and only suitable for measuring the impedance of single cells or small modules [25], [26]; these drawbacks limit the use of these instruments in research and development.

The impedance spectroscopy measurement of a battery can be performed by applying a small excitation signal at a frequency of interest to the battery and then observing the response signal. Notably, the frequency of interest can be varied within a suitable range to obtain a useful impedance spectrum for the battery. In addition, the response signal generally possesses the same frequency and shape as the excitation signal, but it shows a shift in phase. Based on the current response and voltage excitation, battery impedance is determined as

where

The responses of a battery with respect to perturbation signals differ depending on the state of the battery. Therefore, the electrochemical impedance determined with Eq. (1) can be utilized to determine the state of the battery.

As previously mentioned, excitation and response signals are typically small (in the scale of millivolts or milliamps); hence, measurement requires filtering out all unexpected signals and noises. In the current study, a DLIA was adopted to extract the signals at the frequency of interest. This DLIA is preferable because of its high performance in measuring small signals regardless of the high level of noise [27].

An AC signal superimposed on a DC signal and noises, u(n), can be represented in a discrete form as

The DLIA generates two orthogonal sinusoidal reference signals at each frequency as excitation signals generated numerically as Eq. (3). These numeric reference signals are immune to noise [28].

The in-phase and quadrature-phase quantities are obtained by multiplication of the measured signal and sine and cosine reference signals, respectively.

By applying a moving average filter to eliminate the AC components in Eqs. (4) and (5), the target signal can be extracted with the magnitude determined in Eq. (6) and the phase determined in Eq. (7).

The complex form of the battery impedance can be determined with Eqs. (8) to (9).

Typically, the perturbation signal is swept within the desired frequency range (from 0.1 Hz to 1.0 kHz in this study), after which the impedance data are calculated. The parameters of the equivalent circuit of the lead–acid battery is then obtained based on the obtained impedance data.

B. SOH Estimation Using Extracted Parameters from Electrochemical Impedance

A popular equivalent circuit model of a lead–acid battery is shown in Fig. 1 [29]-[31]. All the electrochemical reactions in a lead–acid battery can be represented by the elements in this equivalent circuit model. Rs is the ohmic resistance that reflects the conductivity of the electrolyte and electrical pathway. Rct and Cdl are charge transfer resistance and double layer capacitance, respectively, which describe the transient behaviors caused by the charge transfer reaction. ZW is the Warburg impedance that reflects battery diffusion. Aside from usage, batteries age because of chemical processes, such as anodic corrosion, positive active mass degradation, irreversible formation of lead sulfate in active mass, short circuits, and loss of water [32]. These processes result in changes in equivalent circuit parameters.

Fig. 1.Equivalent circuit model of a lead–acid battery.

Battery aging is accompanied by an increase in ohmic resistance and a decrease in capacity. If these parameters can be extracted from the impedance spectrum, SOH can be estimated based on variations in parameter values in the equivalent circuit of the battery over the aging process. A method to estimate the SOH of an arbitrary battery using the parameters of its equivalent circuit was introduced in [13]; the equivalent circuit parameters of a battery in fresh and fully aged conditions were used to estimate SOH.

The SOH of an arbitrary battery may also be estimated using its ohmic resistance, as shown in Eq. (10) [13].

where

However, Eq. (10) is only valid under the assumption that the relationship between the increase in ohmic resistance and the remaining capacity is linear.

In [27], an advanced method to estimate the life span of a fuel cell by using its cathode time constant (a product of cathode resistance and capacitance) was introduced. Unlike the method in [13], this advanced method does not require strict linearity in the variation of the parameters of the battery equivalent circuit.

In this study, the least squares algorithm was used to determine the equivalent parameters from the best-fit curve of the model data to the measured data. Given that impedance data show a complex form, a complex nonlinear least squares (CNLS) fitting method was adopted to extract the battery parameter values. The CNLS method is a Levenberg–Marquardt least squares method applied to complex numbers. The equivalent circuit model of the battery in Fig. 1 and actual impedance data are the inputs to this method [33]. This method finds the best-fit curve with the model parameters by minimizing the error between the measured and model curves through iterative calculation.

The equivalent circuit model of the battery in Fig. 1 has complex impedance as a function of frequency and parameters, as demonstrated in Eq. (11).

In Eq. (11), Rs, Rct, Cdl, and ZW are the parameters of the equivalent circuit model for the lead–acid battery estimated by minimizing the function “Φ”.

The Taylor series method can calculate impedance based on the previous impedance value and the variations in the approximated parameters. The estimated parameters can be updated with variation Δ by using Taylor series expansion, as shown in Eq. (13).

The values of ΔRs, ΔRct, ΔCdl, and ΔZW are then determined with Eq. (14).

where

The abovementioned fitting algorithm can be implemented by an iterative loop in a digital signal processor (DSP). The model parameters Rs, Rct, Cdl, and ZW are initialized in the first loop. In the next iteration, all model parameters are updated based on the calculations. When the value of Φ converges to a certain limit, that is, 10−6 in this study, the value that best fits the battery model parameters is obtained [34].

 

III. STRUCTURE AND OPERATION OF THE PROPOSED INTELLIGENT CHARGER WITH AN EMBEDDED BATTERY DIAGNOSIS FUNCTION

Fig. 2 illustrates a block diagram of the proposed intelligent charger with an embedded diagnosis function that uses online impedance spectroscopy. The charger is composed of a bidirectional DC/DC converter and a DSP controller that implements both CC/CV charge and battery diagnosis function using EIS. We used a low-frequency transformer and a non-isolated bidirectional converter for simple structure. Nevertheless, other types of bidirectional converters, including high-frequency transformers, can be used in high-power applications with galvanic isolation without limitations.

Fig. 2.Block diagram of the proposed intelligent charger.

The proposed charger has two different operating modes (Fig. 3). In the charge operation, the CC/CV charging method is applied to fully charge a battery. Thereafter, the impedance spectroscopy method is applied to investigate the impedance spectrum of the battery.

Fig. 3.Operation of the proposed intelligent charger.

To limit the maximum charge current, the battery was initially charged in the CC mode with the rated value (i.e., C/10 in this case) from its specification recommended by the manufacturer. When the battery voltage reached 14.4 V, the CV mode was applied to the battery until the charge current decreases to the cut-off value (i.e., 0.02 C in this case).

After the battery was fully charged, it was allowed to rest for 2 hours to obtain the steady state in terms of charge, concentration, and temperature before EIS measurement [35].

To determine the impedance spectrum of the battery, the battery was excited by a small voltage perturbation generated by the voltage controller of the charger; the current response was measured [36]. The AC impedance of the battery at the frequency of interest was effectively extracted by the DLIA embedded in the DSP. In one cycle of perturbation, the battery was charged and discharged equally through the bidirectional converter. Therefore, the charge inside the battery remained the same before and after the test, thereby ensuring the validity of the test. The parameters of the equivalent circuit for the lead–acid battery were obtained with the CNLS method. These parameters were then used to estimate SOH by comparing the parameter values of an aged lead–acid battery with those of a fresh one. When the measured impedance of the battery showed a larger increase than previous results or reached the values of a fully aged battery, the system generated a warning signal for the user to check the battery. As SOH can be monitored automatically and periodically by using the proposed charger, sudden failures of the battery can be avoided. System reliability also increases, thus reducing the cost of possible replacements and maintenance because of sudden battery-related system failures.

 

IV. DESIGN OF THE DIGITAL CONTROLLER FOR THE CHARGER AND EIS FUNCTION

The converter employed in the proposed charger must be bidirectional to generate perturbations for the EIS of a lead–acid battery. During EIS operation, the battery was charged and discharged for half a cycle at the test frequency. The battery charge state must remain unchanged before and after the impedance spectroscopy test; otherwise, the battery parameters would vary. To charge the lead–acid battery from the grid, a buck topology was selected for the charge converter to step down DC-link voltage to the battery voltage. A bidirectional converter (Fig. 2 [37]) can be derived when the freewheeling diode in the buck converter is replaced by an active switch. The specifications of the charge converter are shown in Table I.

TABLE ISPECIFICATIONS OF THE CHARGE CONVERTER

The control-to-output voltage (Gvd) and control-to-inductor current (Gid) transfer functions were derived with a small-signal modeling technique [38] with a simplified R–C model of the lead–acid battery.

To obtain high-accuracy impedance results, the crossover frequency should be sufficiently high to generate a pure sinusoidal perturbation. Thus, the bandwidth of the closed loop system was set to be 10 times higher than the highest frequency perturbation. Since the useful impedance spectrum for the lead–acid battery in the proposed method ranges from 0.1 Hz to 1 Khz, the bandwidth of the voltage loop must be higher than 10 KHz. To attenuate the high-frequency switching components on the closed-loop system, the bandwidth of the closed-current loop system was set to 3 KHz, which is much lower than the switching frequency.

 

V. EXPERIMENTAL RESULTS OF THE PROPOSED INTELLIGENT CHARGER

Fig. 4 shows the experimental setup of the proposed system, which consists of a DC power supply, a 12 V 40 Ah lead–acid battery (ITX40) from the ATLASBX Battery Company [39], and the proposed charger.

Fig. 4.Experimental setup for the performance test of the proposed intelligent charger.

The control algorithms, including CC/CV charge and diagnosis functions, were implemented in a high-performance DSP (TMS320F28335) from Texas Instruments. Fig. 5 shows the CC/CV charge profile of the lead–acid battery obtained by the proposed charger. The lead–acid battery began to get charged in CC mode with its rated charge current (4.0 A, 0.1 C). When the battery voltage reached the maximum charge voltage of 14.4 V, CV mode was applied until the charge current decreased to 0.8 A (0.02 C), which indicated that the battery was fully charged. The battery was allowed to rest for 2 hours. Afterward, EIS investigation of the lead–acid battery was performed. By adding a small sinusoidal perturbation to the reference of the voltage controller, a voltage excitation was generated and injected to the battery terminal.

Fig. 5.Charge and EIS operation of the proposed intelligent charger.

To verify the accuracy of the impedance measured by the proposed charger, we compared the results obtained with the proposed charger with those obtained with a commercial EIS instrument (BPS instrument, Kumho). As shown in Fig. 6, the two sets of results differed slightly, and the chi-square value was 0.91%, which indicates a strong correlation between the two results. The proposed charger was then used to measure the impedances of four similar batteries in different SOH states. Three of the batteries were obtained from an electric vehicle (EV) racing club belonging to the Engineering School of Soongsil University, Seoul, Korea (Fig. 7). These batteries were valve-regulated lead–acid batteries (DF80L) manufactured by Delkor Corporation; their nominal voltage and capacity were 12.0 V and 80 Ah, respectively [40]. The fourth battery was a brand-new unit with the same specifications from the same manufacturer.

Fig. 6.Comparison of the Nyquist impedance plots of the lead–acid battery obtained by the proposed intelligent charger and the BPS instrument.

Fig. 7.Four valve-regulated lead–acid batteries used for SOH investigation.

The three batteries had been used in the same EV under different cycles, periods, and conditions. A record of usage history was unavailable. The fresh battery was labeled as 1, whereas the three aged batteries were labeled as 2, 3, and 4.

To measure the SOH of the batteries, we fully charged all the batteries under CC/CV mode charging and then calculated the ampere–hour capacity with the coulomb counting method while discharging the batteries to the cut-off voltage. All four batteries had 102%, 87.5%, 82.5%, and 45% SOH at room temperature. Battery impedance was then measured with the proposed charger. The EIS operation was performed for all four batteries to determine the variation in the ohmic resistance and the other parameters of the equivalent circuit model for the batteries. Fig. 8 shows the Nyquist plots of the four batteries. The impedance plots of batteries 1 to 3 are similar in shape. However, they tend to shift to the right on the real axis, indicating increments in the ohmic resistance (Rs in Fig. 1) of the batteries. The extracted parameter values are listed in Table II. The ohmic resistances of batteries 1 to 4 were 2.13, 2.97, 3.43, and 12.43 mΩ. Fig. 9 shows that the ohmic resistance Rs value increases as the capacity decreases and significantly, increases as the battery becomes fully aged. However, as the relationship between ohmic resistance and battery capacity is not linear, applying Eq. (10) to calculate the exact value of battery capacity is impossible.

Fig. 8.Nyquist plots of the sample batteries obtained by the intelligent charger.

TABLE IIEXTRACTED PARAMETERS OF THE BATTERY EQUIVALENT CIRCUIT MODELS BY USING THE PROPOSED CHARGER

Fig. 9.Ohmic resistance values of the sample batteries.

The relationship between battery capacity and the other parameters was also investigated. Warburg impedance was excluded from this investigation because its value varied only slightly for each battery. Figs. 10 and 11 show the variations in the charge transfer resistance and double layer capacitance of each battery. Considering that the variations are nonlinear with respect to capacity, these parameters cannot be utilized to estimate battery capacity. Therefore, obtaining the accurate relationship between parameter variations and battery capacity using a single parameter of the battery equivalent circuit model is impossible.

Fig. 10.Charge transfer resistances of the sample batteries.

Fig. 11.Double layer capacitances of the sample batteries.

A method to estimate the lifetime of electrochemical energy sources by using the time constant was recommended in [41]. The time constant, a product of the charge transfer resistance and double layer capacitance of the equivalent circuit model, ultimately indicates the electrochemical reaction rate occurring inside an electrochemical energy device. Fig. 12 shows the variation in the time constant for each battery. Evidently, the time constant increases as the battery ages. This trend suggests that the time constant may be used as a reliable indicator of battery aging, as the relationship between variations in parameter value and capacity is linear (Fig. 12). However, because this test only used four batteries, we cannot sufficiently argue that the capacity or SOH can be determined by detecting variations in the aforementioned parameter value. To obtain the accurate relationship between the capacity and parameter variations, more batteries must be tested in future research. Nevertheless, the proposed charger can periodically measure the time constant of a battery, compare it with a reference value, and generate a warning for users to check the battery before it reaches the critical condition. The proposed charger can also significantly reduce the maintenance costs of battery-based systems, thereby increasing system reliability.

Fig. 12.Time constant values of the sample batteries.

 

VI. CONCLUSIONS

A novel intelligent battery charger with an embedded battery diagnosis function using online impedance spectroscopy was proposed. The impedance spectrum of a lead–acid battery can be measured, and any variation in impedance can be detected successfully with the proposed charger. Given that the proposed method can be implemented with no additional hardware, the cost of the proposed charger relative to that of conventional chargers is low. With the proposed charger, battery SOH can be monitored automatically and periodically, and sudden battery failures can be avoided. The use of the proposed charger also increases the reliability of battery-based systems and reduces the costs for replacement and maintenance.