Online Embedded Impedance Measurement Using High ... - IEEE Xplore

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 51, NO. 1, JANUARY/FEBRUARY 2015

Online Embedded Impedance Measurement Using High-Power Battery Charger Yong-Duk Lee, Student Member, IEEE, Sung-Yeul Park, Member, IEEE, and Soo-Bin Han, Member, IEEE

Abstract—This paper presents a new functionality for highpower battery chargers by incorporating an impedance measurement algorithm. The measurement of battery impedance can be performed by the battery charger to provide an accurate equivalent model for battery management purposes. In this paper, an extended control capability of the onboard battery charger for electric vehicles is used to measure the online impedance of the battery. The impedance of the battery is measured by the following: 1) injecting ac current ripple on top of the dc charging current; 2) transforming voltage and current signals using a virtual α−β stationary coordinate system, a d−q rotating coordinate system, and two filtering systems; 3) calculating ripple voltage and current values; and 4) calculating the angle and magnitude of the impedance. The contributions of this paper are the use of the d−q transformation to attain the battery impedance, theta, and its ripple power, as well as providing a controller design procedure which has impedance measurement capability. The online impedance information can be utilized for diverse applications such as the following: 1) a theta control for sinusoidal current charging; 2) the quantifying of reactive current and voltage; 3) ascertaining the state of charge; 4) determining the state of health; and 5) finding the optimized charging current. Therefore, the benefit of this method is that it can be deployed in already existing high-power chargers regardless of battery chemistry. Validations of the proposed approach were made by comparing measurement values by using a battery charger and a commercial frequency response analyzer. Index Terms—d−q transformation, high-power battery charger, impedance measurement.

I. I NTRODUCTION

T

HE rechargeable battery is a pertinent element of the modern electrical industry. The rapid growth of portable devices and electric vehicles is remarkable [1]. In addition, grid-scale battery energy storages for smart grids and microgrids are on the rise. This rapid growth has demanded that batteries possess long life cycles because battery replacement is too expensive. Therefore, it is critically important to extend their life cycle as much as possible [2]–[4]. Manuscript received December 4, 2013; revised May 31, 2014; accepted June 15, 2014. Date of publication July 15, 2014; date of current version January 16, 2015. Paper 2013-IPCC-0969.R1, presented at the 2012 IEEE Energy Conversion Congress and Exposition, Raleigh, NC, USA, September 15–20, and approved for publication in the IEEE T RANSACTIONS ON I NDUSTRY A PPLICATIONS by the Industrial Power Converter Committee of the IEEE Industry Applications Society. Y.-D. Lee and S.-Y. Park are with the Department of Electrical and Computer Engineering, University of Connecticut, Storrs, CT 06269-4157 USA (e-mail: [email protected]; [email protected]). S.-B. Han is with the Energy Saving Laboratory, Korea Institute of Energy Research, Daejeon 305-343, Korea (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIA.2014.2336979

Seeking extended life cycles, many researchers seek to identify the frequency-dependent characteristics of a battery for improving its performance. Battery identification is used for battery modeling which allows estimation of the state of charge (SOC), state of health (SOH), and capacity fading [5]– [13]. In addition, the identification of these characteristics is required for fast and improved charging efficiency. Most intelligent charging approaches are based on battery parameters. Researchers have investigated intelligent charging techniques using a neural network [14], [15], optimization charging [16]– [19], fuzzy control [20], [21], model predictive control [22], pulse charging [23], [24], sinusoidal charging [25], [26], and resistance compensation [27], [28]. Knowing parameters of loss factors related to temperature behavior and the reduction of lithium plating in the battery can be helpful for determining charging/discharging methods. As a result, this brings extended life and efficient energy use [29]–[33]. Most approaches are based on the equivalent circuit of the battery and have been widely used. The impedance parameters of the equivalent circuit inside of a battery are reflective of electrochemical reactions and transport processes. These factors are affected by the internal thermal condition of the battery, charging current, and ionic concentrations. Knowing these parameters is crucial to the management of a battery. Diverse measurement methods of battery parameters to find an equivalent circuit of a battery, such as electrochemical impedance spectroscopy (EIS) [5], [34], model parameter estimation [6]– [10], dynamic battery modeling based on hybrid pulse-power capability [11], and compensated synchronous detection (CSD) [12], [13], have been investigated. Typically, EIS is a representative method for identifying battery parameters. This approach is to apply ac small voltage/ current to a battery and measure its current/voltage response. This process is repeated over a range of frequencies of interest until the spectrum of the impedance is obtained. The impedance of the battery is obtained by analyzing the charging voltage and current using discrete Fourier transforms (DFTs). This method is effective in determining the equivalent circuit. Usually, this DFT-based method is classified into two types: 1) an offline method for analyzing battery impedance by sweeping the input current frequency from hundreds of kilohertz to microhertz [5], [7], [26], [33] and 2) an online method into a battery charger and a battery management system (BMS) for analyzing the operating status of a battery with frequency of kilohertz to hertz [34]. Basically, the offline method requires costly equipment due to high performance characteristics. The online method is less expensive but is limited in its performance

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LEE et al.: ONLINE EMBEDDED IMPEDANCE MEASUREMENT USING HIGH-POWER BATTERY CHARGER

because of high computational burden and limited sampling resolution. The model parameter estimation method is introduced to characterize the model of the online battery’s equivalent circuit. This method depends on the exact equivalent circuit model of the battery. If we know the exact battery model, this method provides the best performance. However, it does not take into account the wideband characteristics of a battery. Therefore, if the model contains information with respect to nonlinear factors, this method may have errors in the estimation of battery parameters. In addition, the computational demand of this method is high compared with other methods because this system is based on a Kalman filter. Estimation approaches are based on the battery model and can estimate the values according to changing parameters. Generally, measurement is a complex procedure and needs external equipment to measure battery parameters. Dynamic battery modeling uses Thevenin’s theorem to create battery models. This approach is to identify the internal resistance of the battery and its voltage source representing the battery’s electromotive force. The voltage source response by pulse current injection can be detected by the time constant of the internal characteristics. Then, this value applies to the Thevenin model, and its parameters can be obtained. From this method, the relaxation effect can be modeled by seriesconnected RC parallel circuits. The open-circuit voltage can be represented as SOC. This method is an accurate model under dynamic current loads. However, this method requires complex computations for identifying battery parameters. The CSD method presents the fastest analysis for identifying battery parameters. This approach parallels EIS in the sense that it injects a range of frequencies as an excitation current. The distinction is that it can obtain the same information in less time. The system response to the noise is processed via correlation and fast Fourier transform (FFT) algorithms. The result is the spectrum of the total response over the desired frequency range. However, in order to produce ac signals using the current/voltage sources with various multifrequencies, the signal generator needs to have precise resolution. It demands the combination of the battery charger as well as the ability to perform the analysis of FFT’s. Some inexpensive methods provide the impedance measurement in BMS. However, it can measure only the ohmic portion of the battery cell. It is strenuous to determine the nonlinear resistance of complex loads because the outcome of the measurement is not only governed by the ohmic behavior of the device, but also, it is affected by its capacitive and inductive behaviors. If additional nonlinearity such as temperature dependence and other time-variant behaviors of the device being tested are considered, it becomes complex to combine in the battery charger or BMS. From a survey of existing approaches and needs of battery identification in the industry, we can summarize the requirements for the next-generation battery charger and the measurement of battery parameters as follows: 1) electrochemical characteristic considerations (activation polarization and concentration polarization); 2) online battery parameter estimation;

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Fig. 1. Proposed battery impedance measurement using a battery charger.

3) implementation visibility in existing systems (cost, computation burden, and simple configuration). From these considerations, if parameters can be measured in an online condition, more frequently updated parameter information will result in better battery utilization. However, it depends on the implementation feasibility and is not easy to achieve by incorporating into other systems with high performance and low cost. The root cause is the computational burden with Fourier transformations, frequency analysis, and sampling time. In addition, its utilizations in many different applications are not yet defined with respect to sweeping frequency range, current level, and so on. In this paper, we propose how to integrate an online embedded impedance measurement function into a battery charger shown in Fig. 1 and analyze the practical use by observing the performance of the battery charger and the accuracy of its impedance measurement. The impedance extracting method used is based on the ac impedance technique. It is implemented by injecting ac ripple current, filtering its response, and calculating the resulting impedance and phase angle. Since the ac technique is a very strong approach, it is a very popular method. In this paper, however, the outstanding point is to use the d−q base approach to attain the battery impedance, theta, and its ripple power. These data can be utilized for diverse applications such as the following: 1) a theta control for sinusoidal current charging [33]; 2) the measurement of ripple power; 3) the quantifying of reactive current and voltage; and 4) the utilization of a phase-locked loop (PLL). In addition, this method is a very popular method in motor drive applications [35] and grid and load impedance measurements [36]. The d−q frame can separate system components such as torque and angular velocity in motor drive applications and active power and reactive power in renewable power inverter applications. Therefore, this method is adopted for the purpose of identifying battery impedance components: both the real part and imaginary part of the impedance and, thus, the magnitude and phase angle of the impedance. Since a high-power battery system is implemented using a digital signal processor and its control loop already contains a d−q transformation loop, the d−q frame approach is computationally advantageous, compared to more traditional signal processing methods. As a result, the impedance extraction is simplified without extra cost. II. BATTERY C HARACTERISTICS General battery characteristics are discussed in order to determine the frequency sweep range and understand its resulting

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From this equation, in order to extract each component, a frequency sweep is applied because the equivalent circuit model has different impedance values with respect to the frequency sweep range shown in Fig. 2(a). Typically, the battery impedance curve can be attained from several kilohertz to sub-hertz. To summarize the behavior of the equivalent circuit, the total battery impedance is analyzed according to the range of sweep frequencies. Typically, at a certain frequency point between the kilohertz and hundreds of hertz range, the total impedance is equal to RO because CDL and Zw become negligibly small, as shown in Fig. 3(a). As a result, current cannot flow through RCT . In addition, at a high frequency over this point, only the inductive element ZLe and the electrolyte resistance RO remain. The total impedance ZT becomes Fig. 2. Characteristics of a battery. (a) Frequency spectra. (b) Equivalent circuit of the battery.

phenomenon. Electrochemical reactions of the battery are classified in the three sections: the conductivity of the electrolyte, the double layer and charge transfer effects on the electrode, and the ion diffusion (or Warburg impedance).

ZT = RO + ZLe .

At the boundary condition frequency between the charging transfer reaction and diffusion, CDL and RCT are of significant magnitude, shown in Fig. 3(b). As a result, the total impedance is ZT (s) = RO +

A. Battery Equivalent Circuit and Definitions In Fig. 2(b), an electrochemical battery model with the classified sections can be represented with resistors and capacitors of an equivalent circuit as follows: 1) the ohmic resistance RO , which is due to the electrolyte resistance; 2) the activation polarization factors RCT and CDL ; and 3) the Warburg impedance ZW , which represents the diffusion due to the concentration polarization. In addition, the parasitic inductance Le can be represented with the battery external/internal connections shown in Fig. 2(b). Typically, the ohmic resistance RO is modeled based on the conductivity of the electrolyte. It depends on the ionic concentration and temperature. This is a geometric characteristic related to ion plating. The layer between the electrode and the electrolyte forms the charge zone for the activation polarization. It is modeled as a charge transfer resistance RCT , which determines the rate of the exchange current with the double layer capacitance CDL in parallel. The stored charge within CDL affects the electrode voltage. From the impedance spectrum, it is possible to deduce the equivalent circuit and determine the significance of the different components. The concentration polarization effect is represented by the Warburg impedance ZW . Inside a battery, the ions are transported by diffusion and migration. Diffusion is generated by the gradient in concentration [29]–[33]. B. Identification of Battery Parameters According to Frequency Response Typically, the equivalent impedance of a battery can be expressed as follows: Z(s) = ZLe + RO +

RCT + Zw . 1 + sCDL RCT

(1)

(2)

RCT . 1 + sCDL RCT

(3)

At moderate frequencies, CDL and RCT can be separated using a characteristic frequency as follows: ωC =

1 . 2πRCT CDL

(4)

Typically, the equivalent circuit, which is to include mass transfer diffusion effects, is shown in Fig. 3(c). The frequency ranges of the concentration polarization and diffusion are very low. Zw is a complex quantity having equal real and imaginary parts. This impedance is proportional to the reciprocal of the square root of the frequency. It is ZT (s) = RO +

RCT + Zw . 1 + sCDL RCT

(5)

Generally, this frequency range is not the same according to each battery chemistry and configuration. However, usually we can estimate these factors within several kilohertz to 0.1 Hz [5], [7], [26], [34]. In Table I, a range of several kilohertz down to the sub-hertz region is recommended. It is notable that switching frequency performance limits the frequency sweep range. III. I MPEDANCE M EASUREMENT M ETHOD The method of online measurement of battery parameters is to first discern the impedance by injecting ac ripple current along with the dc charging current and then to measure the ripple voltage. This can be further broken down into four steps, shown in Fig. 4. The first step is to eliminate the dc component of the battery current and voltage and to make the α−β frame. The second step is to apply a d−q transformation. The third step is to calculate the power of the ripples and the magnitude of the


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Fig. 3. Impedance change with respect to ripple frequency. (a) High-frequency region. (b) Medium-frequency and low-frequency regions. (c) Very low frequency region (typically under 0.1 Hz). TABLE I F REQUENCY R ANGE FOR M EASURING BATTERY I MPEDANCE

Fig. 5. Voltage and current α−β transformation.

fripple of the current ripple and current magnitude Mripple every cycle. It is as follows: HBPF (s) =

Fig. 4.

Overall steps of online impedance extraction.

total impedance. The final step is to calculate the phase angle between the current ripple and the voltage ripple. At the end, imaginary and real impedances are obtained.

s2 +

To separate the magnitude and phase, we use α−β and d−q coordinate systems, which are normally used in threephase systems, for the separation of components. Since this is a single-phase system, it is necessary to create a virtual α−β frame. Fig. 5 shows the α−β stationary coordinate system as the first step. In order to create the ripple current for the virtual α−β frame, the virtual PLL is used, shown in Fig. 5. This step eliminates the dc component by using a bandpass filter (BPF). The output from the BPF becomes the α-axis in the frame. For extracting the proper ripple component, the coefficients of the BPF need to be recalculated with respect to the frequency

ωb2

(6)

where ωb is the center frequency, B is the band frequency, and Q is ωb /B. To make the virtual β-axis, an all pass filter (APF) is used. The APF passes all frequencies equally in gain, but a phase shift of 90◦ is only provided at the pass frequency. Therefore, the virtual α−β frame of this system is made by using an APF HAPF (s) = −

A. Step One: α−β Stationary Coordinate System

ωb Qs ωb Qs+

s − ωc s + ωc

(7)

where ωc is the pass frequency. While performing a frequency sweep, the pass frequency of the filter should be changed with respect to the specified sweep frequency. The proposed system adjusts the filter coefficients for each selected ripple frequency, shown in Fig. 5. Since the ac ripple current is generated by the selected frequency in the controller, the exact beta frame can be obtained. B. Step Two: d−q Rotating Coordinate System Fig. 6 is the second step which shows the d−q transformation. This transformation maps the α−β coordinate systems onto a two-axis synchronous rotating reference frame.

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Fig. 6. Voltage and current d−q transformation.

By obtaining θ from the PLL, the d−q values of the voltage and current are calculated as follows: cos θ −sin θ vα vd = (8) sin θ cos θ vq v β id cos θ −sin θ iα = . (9) sin θ cos θ iq iβ

Fig. 7.

FB-PS-ZVS dc–dc converter and the control block.

Resistance is the real part of the impedance. Reactance is the imaginary part of the impedance. They can be obtained using an expression derived from

C. Step Three: Ripple Power and Total Impedance Calculation In step three, the obtained d−q values of the current and voltage are used for the power calculation to obtain the phase difference between the current and the voltage. To calculate the total impedance vq2 + vd2 |ZT | = . (10) i2q + i2d In addition, φ can be calculated by using the power factor equation. To calculate φ, active and reactive powers of the ripple current and voltage are first calculated as follows: (vq iq + vd id ) (11) 2 (vq id − vd iq ) Qripple = . (12) 2 We can obtain apparent power from the aforementioned power equations as follows: Sripple = Pripple 2 + Qripple 2 . (13) Pripple =

From the active and apparent powers, we can derive the power factor Pripple . (14) P F = cos(φ) = Sripple D. Step Four: Angle and Impedance Calculation In the final step, the power factor value is used for calculating φ. In this manner, we can obtain the phase difference between the charging voltage and current of the battery. This equation is given as follows: Pripple vq = tan−1 . (15) φ = cos−1 Sripple vd

ZT = Zreal + jZimg

(16)

where Zreal = |ZT | cos φ and Zimg = |ZT | sin φ. IV. BATTERY C HARGER D ESIGN WITH I MPEDANCE M EASUREMENT F UNCTIONALITY As a prototype battery charger, Fig. 7 shows a full bridge-phase shift-zero voltage switching (FB-PS-ZVS) dc–dc converter. Typically, the converter is used for high-power applications. In this system, a Li-ion battery module consists of Le , Ro , RCT , and CDL , and Voc , all in series. In addition, the battery module provides information from the BMS such as cell temperature, cell voltage, current of the battery module, and SOC. The information can be transferred by CAN communication. The converter carries out a feedback control from a measured current and voltage, the values are used for online impedance measurement, and the current and voltage controls are based on a PI controller. Typically, the dc current reference is determined by C-rate of the battery. In order to match the measurement current of the frequency response analyzer (FRA) and the proposed system, 0.125 C-rate is used. Generally, the transfer function of the output filter is Ho (s) =

1 s2 L

f Cf

L

f + s Zload +1

(17)

where Lf is the filter inductor and Cf is the filter capacitor. The transfer function of the LC filter is represented as a general term included in the load impedance Zload in (18). In order to obtain a more accurate system model, the battery model, omitting the low-frequency characteristics, is as follows: RCT Zbat (s) = Ro + sLe + . (18) RCT CDL s + 1


TABLE II PARAMETERS OF THE BATTERY AND BATTERY C HARGER

In Ho (s), Zload is replaced with Zbat , which incorporates the battery equivalent circuit parameters in (19). The new transfer function with respect to our battery model is Ho (s) =

=

503

1 s2 L

b0

f Cf

s4

+s

Lf

Ro + sLe + R

RCT CT CDL s+1

+1

a0 s 2 + a 1 s + a2 + b1 s 3 + b2 s 2 + b3 s + a 2

(19)

where a0 = CDL Le RCT a1 = Le + CDL RCT Ro a2 = RCT + Ro b0 = Lf Cf Le CDL RCT b1 = Cf Le Lf + CDL Cf Lf RCT Ro b2 = CDL Le RCT + CDL Lf RCT + Lf Cf RCT + Lf Cf Ro where n is the turns ratio, Vin is the input dc voltage, and Llk is the leakage inductance of the high-frequency transformer. The control-to-filter inductor current transfer function is

b3 = Le + Lf + CDL RCT R. The input impedance of the output filter is L

Zf (s) =

f +1 Zbat s2 Lf Cf + s Zbat

1 + sZbat Cf 4

=

Gid (s) =

3

=

2

a0 s + a1 s + a2 s + a3 s + a4 b0 s 3 + b 1 s 2 + b 2 s + 1

(20)

a0 = Lf Cf Le CDL RCT a1 = Cf Le Lf + CDL Cf Lf RCT Ro a2 = CDL Le RCT + CDL Lf RCT + Lf Cf RCT + Lf Cf Ro a3 = Le + Lf + CDL RCT Ro a4 = RCT + Ro b0 = CDL Cf Le RCT b1 = Cf Le + CDL Cf RCT Ro b2 = CDL RCT + Cf RCT + Cf Ro . Typically, the control-to-output transfer function is Zf vˆo (s) = Ho nVin ˆ Zf + 4n2 Llk fs d(s)

Gid (s) =

3.419 ×

a0 s 3 + a1 s 2 + a2 s + a3 b0 s 4 + b 1 s 3 + b 2 s 2 + b 3 s + b4

(21)

a0 a1 a2 a3 b0 b1

= CDL Lf Le RCT Vin n = Cf Le Vin n + CDL Cf RCT Ro Vin n = CDL RCT Vin n + Cf RCT Vin n + Cf Ro Vin n = Vin n = CDL Cf Le Lf RCT = 4CDL Cf Le Llk RCT fs n2 + Cf Le Lf + CDL Cf Lf RCT RO b2 = CDL Le RCT + CDL Lf RCT + Lf Cf RCT + Lf Cf Ro + 4Cf Le Llk fs n2 + 4CDL Cf Llk RCT RO fs n2 b3 = Le + Lf + CDL RCT RO + 4CDL Llk RCT fs n2 + 4Cf Llk RCT fs n2 + 4Cf Llk RO fs n2 b4 = 4Llk fs n2 + RCT + RO .

In order to analyze stability between the battery and converter, the parameters of Table II are used. These values are from existing FRA equipment and the designed FB-PS-ZVS dc–dc converter. Le , RO , RCT , and CDL are measured using Model 1260 of Solartron Analytical. From the parameters, the control-to-inductor current transfer function is shown in (23) at the bottom of the page.

1.389 × 10−11 s3 + 3.86 × 10−8 s2 + 1.034s + 325 + 1.964 × 10−12 s3 + 2.558 × 10−6 s2 + 0.1399s + 43.74

10−17 s4

(22)

where

where

Gvd (s) =

ˆiL (s) nVin = ˆ Z + 4n2 Llk fs f d(s)

(23)

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Fig. 8. Control-to-filter inductor current transfer function. (a) Continuous and discrete time transfer functions of plant and open-loop transfer function. (b) Step response of the closed-loop system.

Fig. 9. α−β stationary coordinate system. (a) Battery voltage. (b) Battery current. (c) α−β frame for battery current. (d) α−β frame for battery voltage.

In order to implement the proposed system, a digital signal processor is used. Exact performance analysis is required in the discrete time domain. The transfer function of the plant is converted from the s-domain to the z-domain as follows: Gid (z) =

6.948z 3 − 12.8z 2 + 11.95z − 5.991 . z 4 − 1.907z 3 + 1.841z 2 − 0.9755z + 0.05657 (24)

In order to carry out the ac sweep, the frequencies of the ripple current are applied from 0.1 Hz to 100 Hz, and the magnitude range is ±1 A. Battery voltage and current are sampled every 50 μs. In order to get a fast response for a 100-Hz sinusoidal current perturbation, a discrete PI compensator is designed as follows: Cid (z) =

0.014772(z + 1) . z−1

(25)

From these results, the open-loop transfer function and closed-loop transfer function are obtained as (26) and (27), shown at the bottom of the page. Fig. 8(a) shows the control-to-filter inductor current transfer function. The system is damped by load impedance. As a result, the resonant pole does not exist in the system. In the z-domain, the open-loop transfer function has a phase margin of 76.6◦ , and the system is stable. Fig. 8(b) shows the step response of the closed-loop transfer function. It has no overshoot and a fast settling time of 0.7 ms. V. A NALYSIS OF I MPEDANCE E XTRACTION U SING S IMULATION The MATLAB simulation tool is used to verify the proposed method. The FB-PS-ZVS dc–dc converter is adopted for the

Topenloop (z) =

0.1026z 4 − 0.08643z 3 − 0.01249 × 10−5 z 2 + 0.08806z − 0.08851 z 5 − 2.907z 4 + 3.749z 3 − 2.817z 2 + 1.032z − 0.05657

(26)

Tclosedloop (z) =

0.1026z 4 − 0.08643z 3 − 0.01249 × 10−5 z 2 + 0.08806z − 0.08851 z 5 − 2.805z 4 + 3.662z 3 − 2.829z 2 + 1.12z − 0.1451

(27)


Fig. 10. d−q rotating coordinate system. (a) d−q values of the current ripple of the battery. (b) d−q value of the voltage ripple of the battery.

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Fig. 12. Impedance plot. (a) Total extracted impedance. (b) Imaginary part. (c) Real part.

The final step is to extract the imaginary and real impedances shown in Fig. 12. The total impedance can be calculated from these two values inversely. That equation is rearranged to |ZT | =

2 2 Zreal + Zimg = RO +

RCT . 1 + ωRCT CDL

(28)

Fig. 12 shows the extracted impedance values. Fig. 12(a) shows the total extracted impedance ZT . The imaginary part Zimg and real part Zreal are shown in Fig. 12(b) and (c), respectively. VI. E XPERIMENTAL R ESULT Fig. 11. Total impedance. (a) Active power. (b) Reactive of ripples. (c) Power factor of ripple power. (d) Phase difference.

charger. The perturbation signal needed for impedance extraction consists of ripple current of 100 Hz with fluctuations in magnitude of ±1 A. The first step is to make the α−β frame shown in Fig. 9. The battery current Ibat and voltage Vbat contain a dc component and an ac ripple component. In Fig. 9(a), Ibat contains 5 A dc, which is superposed with the ±1 A ripple. When the current is injected, the ac component of the voltage response is ±0.014 V, as shown in Fig. 9(b). The dc components of these values are eliminated through the BPF. As you can see in Fig. 9(c) and (d), the output values take exact ripple values. In addition, the α−β frame has 90◦ difference angles. From these results, its angle difference is checked in Fig. 9(c) and (d). The second step is the d−q transformation. From this method, vd , vq , id , and iq values are obtained. vd and id have peak values of vα and iα , respectively. vq and iq are vectors in the q-axis, which is orthogonal to the d-axis. Fig. 10(a) shows id and iq . The third step is to calculate the total impedance of the battery. This value is used for calculating the active/reactive power of the ripple from the battery voltage and current. Fig. 11(a) and (b) shows the active power P and reactive power Q of the ripple. From these values, we can obtain the power factor of the ripples and can calculate φ, shown in Fig. 11(c) and (d), respectively.

Table II displays the experimental parameters. In order to match the current level with the FRA, 5 Adc and ±1 A are superposed for the injected battery current, shown in Fig. 13(a). Its ripple frequency is 40 Hz. Fig. 13 shows the first step, which is to make the α−β frame. Fig. 13(a) shows the output results of the BPF and APF from the battery voltage. Fig. 13(b) shows the output results of the BPF and APF from the battery current. As a result, the α−β frame is obtained, and its phase delay between α and β is 90◦ . Fig. 14 shows step two for the d−q transformation output. Fig. 14(a) shows the d−q values of the current in the actual experiment. Fig. 14(b) shows the d−q values of the voltage. From the third and fourth steps, the impedance of the battery is obtained. In addition, the magnitude response of the battery voltage ranges from 7 to 20 mV. When the analog signal is digitized, the measurement resolution determines the maximum possible signal-to-noise ratio (SNR). If we consider an error of 2 b and if the input voltage VS and noise voltage VN are 7 and 1.5 mV, respectively, the SNR is SNRdB = 20 log10 (VS /VN ) = 13.6 dB.

(29)

Therefore, the range of SNR for the voltage measurement is acceptable with 13.6 dB. The proposed system creates sinusoidal ripple currents from 0.1 to 100 Hz. From these frequency sweeps, the battery charger obtains the battery impedance. Fig. 15 shows the impedance change according to the ac sweep ripple current. The frequency

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Fig. 13. Waveform measurement of the α−β stationary coordinate system. (a) Battery voltage. (b) Battery current.

Fig. 14. Waveform measurement of the d−q frame. (a) d−q values of the current ripple of the battery. and (b) d−q values of the voltage ripple of the battery.

real impedance through a frequency sweep from 0.1 to 100 Hz. The red line is the real impedance found by the FRA, and the dashed blue line is the measured real impedance. As a result, an error of max 1 mΩ occurred due to ADC resolution and low magnitude of voltage ripple response. Fig. 16(b) shows a result of imaginary impedance. The red line is the imaginary impedance detected by the FRA, and the dashed blue line is the imaginary impedance measured by the proposed system. From these results, the imaginary impedance is minimized at a frequency of 1 Hz. This means that there is a boundary between the concentration polarization and activation polarization. From this result, the proposed system is validated.

VIII. C ONCLUSION Fig. 15. Impedance spectroscope according to SOC.

is changed from 0.1 to 100 Hz, and SOCs are measured from 10% to 80%. VII. C OMPARING THE E XISTING I MPEDANCE A NALYZER TO THE P ROPOSED M ETHOD In order to verify the proposed system, the result is compared to the results of the existing FRA and Model 1260 of Solartron Analytical. Fig. 16 shows the comparative data from the proposed system and existing FRA. Fig. 16(a) shows the

This paper has presented a method of measuring the impedance of a battery using a high-power battery charger. Since high-power battery chargers are usually designed with high-performance digital signal processors and voltage/current measurement circuitry, the impedance of the battery stack may be measured and utilized in a BMS. Therefore, we expect that the battery impedance measurement can be embedded in battery chargers as a no-cost auxiliary function. In order to obtain high performance of a battery, the best approach is to analyze an equivalent circuit of the battery. Generally, conventional approaches are difficult to combine


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Fig. 16. Comparison data with commercial FRA and the proposed system. (a) Real impedance. (b) Imaginary impedance.

into the battery charger and are independent from the charger itself because analyzers are very expensive and have complex configurations. In order to overcome these restrictions, a highpower battery charger with an online embedded impedance measurement feature is proposed. From the paper contents, the summary is as follows.

Finally, since most electrochemical batteries have similar characteristics, the proposed impedance extraction method can be applicable to the other battery chemistries without requiring any adjustments.

1) Existing methods are analyzed, and their strengths and demerits are deduced. 2) From analyzed data, the research needs are deduced. 3) Frequency sweep ranges are analyzed for determining system limitations. 4) α−β and d−q base transformations are used for the impedance measurement. 5) The battery charger is analyzed for the control of the highfrequency ripple current. 6) Simulation and experiments validate the proposed method. 7) Impedance values are measured according to the frequency sweep and SOC. 8) Results are verified with Solartron equipment.

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As a result, the proposed method has overall strength due to the online embedded implementation. However, due to the limitations of converter switching frequency, the battery equivalent circuit model could not be constructed. Despite this, the given experimental results display the feasibility and accuracy of the impedance measurement using a high-power battery charger which may suffer from the same limitations. From these results, we summarize the benefits of this system. 1) Integration of impedance measurement in the battery charger. 2) Diverse utilization a) Extracted output values can be used such as SOC, SOH, and high-performance charging algorithms. b) A theta control for the sinusoidal current charging. c) The measurement of ripple power and the quantifying of reactive current and voltage. d) The utilization of the PLL. 3) It is a low-cost implementation for high-powered battery systems with dynamic electrochemical considerations.

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Yong-Duk Lee (S’06) received the B.S. degree in electronic engineering and the M.S. degree in electrical engineering from Hankyong National University, Anseong, Korea, in 2006 and 2008, respectively. He has been working toward the Ph.D. in power electronics at the University of Connecticut, Storrs, CT, USA, since 2011. From 2007 to 2010, he was an Associate Researcher with POSCO ICT.

Sung-Yeul Park (S’04–M’09) received the M.S. and Ph.D. degrees in electrical and computer engineering from Virginia Polytechnic Institute and State University (Virginia Tech), Blacksburg, VA, USA, in 2004 and 2009, respectively. From 2002 to 2004, he was a Graduate Research Assistant with the Center for Rapid Transit Systems, Virginia Tech. From 2004 to 2009, he was a Graduate Research Assistant with the Future Energy Electronics Center (FEEC), Virginia Tech. He joined the University of Connecticut, Storrs, CT, USA, as an Assistant Professor in the Department of Electrical and Computer Engineering and as an Associate Member of the Center for Clean Energy Engineering in 2009. His research interests include energy-efficient energy and power conversion, renewable and distributed generation integration, smart buildings, and microgrid applications. Dr. Park has received several international paper awards including a third paper award at the 2004 IEEE Industry Applications Society Annual Meeting, a best paper award at IEEE Power Conversion Conference (IPCC) 2007, an outstanding writing award in the International Future Energy Challenge (IFEC) in 2007, and a Torgersen Research Excellence Award from the College of Engineering, Virginia Tech, in 2009.

Soo-Bin Han (M’95) was born in Korea in 1958. He received the B.S. degree in electronic engineering from Hanyang University, Seoul, Korea, in 1981 and the M.S. and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology, Daejeon, Korea, in 1986 and 1997, respectively. He has been a Principal Researcher with the Korea Institute of Energy Research, Daejeon, since 1986. He has performed various national projects as a project manager including fuel-cell power application, advanced lighting, and new energy saving technology. His current research interests include energy storage technology and resilient microgrid systems. Dr. Han is a member of the Korean Institute of Power Electronics, the Korea Institute of Illuminating and Electrical Installation Engineers, and the Korean National Committee of CIE.