on-line Embedded Impedance Measurement Using High Power Battery Charger

8/10/2019 on-line Embedded Impedance Measurement Using High Power Battery Charger

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10.1109/TIA.2014.2336979, IEEE Transactions on Industry Applications

On-line Embedded Impedance Measurement using High Power Battery Charger

Yong-Duk LeeStudent Member, IEEE

University of Connecticut371 Fairfield Way

Storrs, CT 06269-2157 [email protected]

Sung-Yeul ParkMember, IEEE

University of Connecticut371 Fairfield Way

Storrs, CT 06269-2157 [email protected]

Soo-Bin HanMember, IEEE

Korea Institute of Energy Research152 Gajeong-ro, Yuseong-gu

Daejeon, 305-343 South [email protected]

Abstract -- This paper presents new functionality for high

power 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 on-board

battery charger for electric vehicles is used to measure on-line

impedance of the battery. The impedance of the battery is

measured by 1) injecting ac current ripple on top of the dc

charging current, 2) transforming voltage and current signals

using a virtual - stationary coordinate system, 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

research 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 on-line impedance information can

be utilized for diverse applications, such as 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 Impedance measurement, high power battery

charger, d-q transformation.

I. ITRODUCTION

The 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].

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), the 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 temperaturebehavior 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 the 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 an 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 off-line method for analyzing battery impedance

by sweeping input current frequency of from hundreds of

kHz to Hz [5, 7, 26, 33], and (2) an on-line method into a

battery charger and a battery management system (BMS) for

analyzing the operating status of a battery with frequency of

kHz to Hz [34]. Basically, the off-line method requires costly

equipment due to high performance characteristics. The on-

line method is less expensive, but is limited in its

performance because of high computational burden and






limited sampling resolution.

The model parameter estimation method is introduced to

characterize the model of the on-line batterys equivalent

circuit. This method depends on the exact equivalent circuitmodel 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

non-linear 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 Thevenins theorem tocreate battery models. This approach is to identify the internal

resistance of the battery and its voltage source representing

the batterys 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 series connected 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 foridentifying 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 multi-frequencies, 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 FFTs.

Some inexpensive methods provide the impedance

measurement in BMS. However, it can measure only theohmic portion of battery cell. It is strenuous to determine the

non-linear 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 non-linearity 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:

Electrochemical characteristics considerations(Activation polarization and concentration polarization)

On-line battery parameter estimation

Implementation visibility in existing systems(Cost, computation burden and simple configuration)

From these considerations, if parameters can be measured

in an on-line 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 on-lineembedded 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. This data can be utilized for diverse

applications such as (1) a theta control for sinusoidal currentcharging [33], (2) the measurement of ripple power, (3) the

quantifying of reactive current and voltage, and (4) 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 digitalsignal 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.

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






II. BATTERY CHARACTERISTICS

General battery characteristics are discussed in order to

determine the frequency sweep range and understand its

resulting phenomenon. Electrochemical reactions of thebattery are classified in the three sections: the conductivity of

the electrolyte, the double layer and charge transfer effects on

the electrode, and ion diffusion (or Warburg impedance).

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)

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 isrepresented 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].

Fig. 2. Characteristics of battery: (a) frequency spectra, (b) the equivalentcircuit of battery

B. Identification of battery parameters according tofrequency response

Typically, the equivalent impedance of a battery can be

expressed as follows:

( )1

CTLe O w

DL CT

RZ s Z R Z

sC R

(1)

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 Fig. 2 (a). Typically, thebattery impedance curve can be attained from several kHz to

sub-Hz. 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 kHz and hundreds of Hz range, the total

impedance is equal to RO because CDL and Zw become

negligibly small 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:

T O Le

Z R Z (2)

At the boundary condition frequency between the charging

transfer reaction and diffusion, CDLandRCTare of significant

magnitude, shown in Fig. 3 (b). As a result, total impedance

is

( )1

CTT O

DL CT

RZ s R

sC R

(3)

At moderate frequencies, CDL and RCT can be separated

using a characteristic frequency as follow:

1

2C

CT DLR C

(4)

Typically, the equivalent circuit, which is to include masstransfer diffusion effects, is shown in Fig 3 (c). The

frequency ranges of the concentration polarization and

diffusion are very low.Zwis 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

( )1

CTT O w

DL CT

RZ s R Z

sC R

(5)

Fig. 3. Characteristics of battery: (a) frequency spectra, (b) the equivalentcircuit of battery

Generally, this frequency range is not the same according

to each battery chemistry and configuration. However,

usually we can estimate these factors within several kHz to

0.1Hz [5, 7, 26, 34]. In Table.I, a range of several kHz down

to the sub-Hz region is recommended. It is notable that

switching frequency performance limits the frequency sweep

range.

TABLEI






FREQUENCY RANGE FOR MEASURING BATTERY IMPEDANCE

ReferenceFrequency for the

electrolyte resistanceCharacteristic

frequencyDiffusion starting

frequency

[5] 285.7Hz 0.3Hz 0.02Hz

[7] 1kHz 150Hz 5Hz[26] 1~1.2kHz N/A N/A

[34] 1.042kHz N/A Above 0.32Hz

III. TECHNICAL WORK PREPARATION

The method of on-line measurement of battery parameters

is to first discern the impedance by injecting ac ripple current

along with the dc charging current, and then measure the

ripple voltage. This can be further broken down into four

steps, shown in Fig.4.

Fig. 4. Overall steps of on-line impedance extraction

The first step is to eliminate the dc component of battery

current and voltage and to make the - 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

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.

A. Step one: -stationary coordinate system

To separate the magnitude and phase, we use -and d-q

coordinate systems, which are normally used in 3-phase

systems, for the separation of components. Since this is a

single-phase system, it is necessary to create a virtual -

frame.

Fig.5 shows the - stationary coordinate system as the

first step. In order to create the ripple current for the virtual

-frame, the virtual phase locked loop (virtual PLL) is used,

shown in Fig. 5. This step eliminates the dc component by

using a band pass filter (BPF). The output from the BPF

becomes the -axis in the frame. For extracting the properripple component, the coefficients of the BPF need to be

recalculated with respect to the frequency,frippleof the current

ripple and current magnitude, Mripple every cycle. It is as

follows:

2 2( ) b bBPF bH s s s sQ Q

(6)

where, bis the center frequency,Bis the band frequency

and Qis b/B.

Fig. 5. Voltage and current -transformation

To make the virtual -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 -frame of this system is made by using an APF.

( ) cAPFc

sH ss

(7)

where cis 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 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 -coordinatesystems onto a two-axis synchronous rotating reference

frame. By obtaining from the phase locked loop (PLL), d-q

values of voltage and current are calculated as follows:

cos sin

sin cos

d

q

v v

v v

(8)

cos sin

sin cos

d

q

i i

i i

(9)

Fig. 6. Voltage and current d-q transformation

C. Step three: Ripple power and total impedancecalculation

In the step three, the obtained d-q values of current and

voltage are used for the power calculation to obtain the phase






difference between current and voltage. To calculate the total

impedance:

2 2

2 2

q dT

q d

v vZi i

(10)

In addition, can be calculated by using the power factor

equation. To calculate , active and reactive power of the

ripple current and voltage are first calculated as follows:

( )

2

q q d d

ripple

v i v iP

(11)

( )

2

q d d q

ripple

v i v iQ

(12)

We can obtain apparent power from the above power

equations as follows:

2 2

ripple ripple rippleS P Q (13)

From the active and apparent power, we can derive the

power factor.

cos( )ripple

ripple

PPF

S (14)

D. Step four: angle and impedance calculation

In the final step, the power factor value is used for

calculating . In this manner, we can obtain the phase

difference between the charging voltage and current of the

battery. This equation is given as follows:

1 1cos ( ) tan ( )ripple q

ripple d

P v

S v (15)

Resistance is the real part of impedance. Reactance is the

imaginary part of the impedance. They can be obtained using

an expression derived from:

eT r al img Z Z jZ (16)

where e cosr al T Z Z and sinimg T Z Z .

IV. BATTERY CHARGER DESIGN WITH IMPEDANCEMEASUREMENT FUNCTIONALITY

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

ofLe,Ro,RCTandCDL, and Voc, all in series. In addition, the

battery module provides information from the battery

management system such as cell temperature, cell voltage,

current of the battery module and the 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 on-line 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 [37]

2

1( )

1o

f

f f

load

H sL

s L C sZ

(17)

whereLfis the filter inductor, Cfis the filter capacitor.

Fig. 7. FB-PS-ZVS dc-dc converter and the control block

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, thebattery model, omitting the low frequency characteristics, is

as follows:

( ) ( )1

CTbat o e

CT DL

RZ s R sL

R C s

(18)

In, ( )oH s ,Zloadis replaced withZbat, which incorporates the

battery equivalent circuit parameters in (19). The new

transfer function with respect to our battery model is

2

2

0 1 2

4 3 2

0 1 2 3 2

1( )

1

( )1

of

f fCT

o e

CT DL

H sL

s L C sR

R sLR C s

a s a s a

b s b s b s b s a

(19)

where

0 1 2

0 1

2

3

, ,

,

dl e ct e dl ct o ct o

f f e dl ct f e f dl f f ct o

dl e ct dl f ct f f c t f f o

e f dl ct

a C L R a L C R R a R R

b L C L C R b C L L C C L R R

b C L R C L R L C R L C R

b L L C R R

Input impedance of the output filter is






2

4 3 2

0 1 2 3 4

3 2

0 1 2

1

( )1

1

f

bat f f

batf

bat f

LZ s L C s

ZZ s

sZ C

a s a s a s a s a

b s b s b s

(20)

where

0 1

2

3 4

0 1

2

,

,

,

f f e dl ct f e f dl f f ct o


e f dl ct o ct o

dl f e ct f e dl f ct o

dl ct f c t f o

a L C L C R a C L L C C L R R

a C L R C L R L C R L C R

a L L C R R a R R

b C C L R b C L C C R R

b C R C R C R

Typically, the control-to-output transfer function is

2

( )( )

4( )

fovd o in

f lk s

Zv sG s H nV

Z n L fd s

(21)

where nis the turns ratio, Vinis the input dc voltage, and

Llk is the leakage inductance of the high frequency

transformer.

The control-to-filter inductor current transfer function is

2

3 2

0 1 2 3

4 3 2

0 1 2 3 4

( )( )

4( )

inLid

f lk s

nVi sG s

Z n L fd s

a s a s a s a

b s b s b s b s b

(22)

where,

0 1

2 3

0

2

1

2

2

,

,

4

4 4

dl f e ct in f e in dl f ct o in

dl ct in f c t in f o in in

dl f e f ct

dl f e lk ct s f e f dl f f ct O


f e lk s dl f lk c

a C L L R V n a C LV n C C R R V n

a C R V n C R V n C R V n a V n

b C C L L R

b C C L L R f n C L L C C L R R

b C L R C L R L C R L C R

C L L f n C C L R

2

2

3

2 2

2

4

4

4 4

4

t O s

e f dl ct O dl lk ct s

f lk ct s f lk O s

lk s ct O

R f n

b L L C R R C L R f n

C L R f n C L R f n

b L f n R R

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,R

O,R

CTand C

DLare measured using

Model 1260 of Solartron analytical.

TABLEIIPARAMETERS OF BATTERY AND BATTERY CHARGER

Parameter Symbol Value Unit

ConverterParameters

Filter inductor Lf 0.8 mH

Filter capacitor Cf 4.8 uF

Filter cut-off frequency fc 2.56 kHz

Leakage inductance Llk 323 uH

Switching frequency fs 20 kHz

Turn ratio n 1.3

Input dc voltage Vin 250 Vdc

Sampling time Tsamp 50 us

Batteryparameters

Cable inductance Le 2.8 uH

Electrolyte resistance or Ro 6.9 m

Ohmic resistance

Charge transfer resistor RCT 1.2 m

Double layer capacitance CDL 2.65 F

From the parameters, the control-to-inductor current

transfer function is

11 3 8 2

17 4 12 3 6 2

1.389 10 3.86 10 1.034 325( )

3.419 10 1.964 10 2.558 10 0.1399 43.74id

s s sG s

s s s s

(23)

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:

3 2

4 3 2

6.948 12.8 11.95 5.991( )

1.907 1.841 0.9755 0.05657id

z z zG z

z z z s

(24)

In order to carry out the ac sweep, the frequencies of theripple current are applied from 0.1 Hz to 100 Hz and the

magnitude range is 1A. Battery voltage and current are

sampled every 50us. In order to get a fast response for a

100Hz sinusoidal current perturbation, a discrete PI

compensator is designed as follows:

0.014772( 1)( )

1id

zC z

z

(25)

From these results, the open-loop transfer function and

closed-loop transfer function are obtained as follows:

4 3 5 2

5 4 3 2

0.1026 0.08643 0.01249 10 0.08806 0.08851( )

2.907 3.749 2.817 1.032 0.05657openloop

z z z zT z

z z z z s

(26)

4 3 5 2

5 4 3 2

0.1026 0.08643 0.01249 10 0.08806 0.08851( )

2.805 3.662 2.829 1.12 0.1451closedloop

z z z zT z

z z z z s

(27)

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 0.7ms.

(a) (b)Fig. 8. Control-to-filter inductor current transfer function: (a) continuousand discrete time transfer functions of plant and open loop transfer function

and (b) step response of the closed loop system






V. TECHNICAL WORK PREPARATION

The MATLAB simulation tool is used to verify the

proposed method. The FB-PS-ZVS dc-dc converter is

adopted for the charger. The perturbation signal needed forimpedance extraction consists of ripple current of 100Hz with

fluctuations in magnitude of 1A.

The first step is to make the -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),Ibatcontains 5 A dc,

which is superposed with the 1A ripple. When the current is

injected, the ac component of the voltage response is

0.014V as shown in Fig. 9 (b). Dc components of these

values are eliminated through the BPF. As you can see in Fig.

9 (c) and (d), output values take exact ripple values. In

addition, the - frame has 90 degree difference angles.

From these results, its angle difference is checked in Fig.9 (c)

and (d).

Fig. 9. -stationary coordinate system: (a) battery voltage, (b) battery

current, (c) -frame for battery current, and (d) -frame for batteryvoltage

The second step is the d-q transformation. From this

method, vd, vq, id, and iq values are obtained. vd and id havepeak values of vand i, respectively. vqand iqare vectors in

the q-axis, which is orthogonal to the d-axis. Fig. 10 (a)

shows idand iq.

Fig. 10. d-q rotating coordinate system: (a) d-q values of current ripple of

battery, and (b) d-q value of voltage ripple of battery

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) show 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 , shown in Fig.11 (c)

and (d), respectively.

Fig. 11. Total impedance: (a) active power, (b) reactive of ripples, (c)power factor of ripple power, and (d) phase difference

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 isrearranged to

2 2

1

CTT real img O

CT DL

RZ Z Z R

R C

(28)

Fig. 12 shows the extracted impedance values. Fig. 12(a)

shows total extracted impedance,ZT. The imaginary part,Zimg,

and real part, Zreal, are shown in Fig.12 (b) and (c),

respectively.

Fig. 12. Impedance plot: (a) total extracted impedance, (b) the imaginary

part, and (c) the real part

VI. EXPERIMENTAL RESULT

Table II displays the experimental parameters. In order to

match the current level with the FRA, 5Adc and 1A are

superposed for the injected battery current, shown in Fig. 13

(a). Its ripple frequency is 40Hz. Fig. 13 shows the first step,

which is to make the -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 -frame is obtained and its

phase delay between and is 90.






Fig. 13. Waveform measurement of -stationary coordinate system: (a)battery voltage, and (d) battery current

Fig. 14 shows step two for the d-q transformation output.

Fig. 14 (a) shows d-q values of the current in the actual

experiment. Fig.14 (b) shows d-q values of voltage.

Fig. 14. Waveform measurement of d-q frame: (a) d-q values of currentripple of battery, and (b) d-q value of voltage ripple of battery

From the third and fourth steps, the impedance of the

battery is obtained. In addition, the magnitude response of the

battery voltage ranges from 7mV to 20mV. When the analog

signal is digitized, the measurement resolution determines the

maximum possible signal-to-noise ratio. If we consider an

error of 2 bits and the input voltage, VS, and noise voltage, VN,are 7mV and 1.5mV, respectively, the SNR is

1020log ( / ) 13.6dB S N SNR V V dB (29)

So the range of SNR for the voltage measurement is

acceptable with 13.6dB.

The proposed system creates sinusoidal ripple currents

from 0.1 Hz to 100Hz. 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 is changed from 0.1 Hz to 100 Hz and

SOCs are measured from 10 to 80%.

Fig. 15. Impedance spectroscope according to SOC

VII. COMPARING THE EXISTING IMPEDANCEANALYZER TOTHE PROPOSED METHOD

In order to verify the proposed system, the result is

compared to the results of the existing FRA and Model 1260of Solartron Analytical. Fig.16 shows the comparative data

from the proposed system and existing FRA. Fig. 16 (a)

shows the real impedance through a frequency sweep 0.1 Hz

to 100 Hz. The red line is the real impedance found by the

FRA and the dashed blue line is the measured real impedance.

Fig. 16. Comparison data with commercial FRA and the proposed system:(a) real impedance, and (b) imaginary impedance

As a result, an error of max 1m 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 1Hz. This means

that there is a boundary between the concentrationpolarization and activation polarization. From this result, the

proposed system is validated.

VIII. CONCLUSION

This paper presents 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 battery management

system. Therefore, we expect 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

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

high-power battery charger with an on-line embedded

impedance measurement feature is proposed. From the paper

contents, the summary is as follows:

Existing methods are analyzed and their strengths anddemerits are deduced.

From analyzed data, the research needs are deduced.






Frequency sweep ranges are analyzed for determiningsystem limitations.

- and d-q base transformations are used for the

impedance measurement. The battery charger is analyzed for the control of the high

frequency ripple current.

Simulation and experiments validate the proposed method.

Impedance values are measured according to the frequencysweep and SOC.

Results are verified with commercial FRA.As a result, the proposed method has overall strength due

to the on-line 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:

Integration of impedance measurement in the batterycharger

Diverse utilization- This result can be used such as SOC, SOH and high

performance charging algorithms.

- A theta control for the sinusoidal current charging.

- The measurement of ripple power and the quantifying of

reactive current and voltage.

- The utilization of the phase locked loop (PLL).

It is a low cost implementation for high-powered batterysystems with dynamic electrochemical considerations.

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.

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on-line Embedded Impedance Measurement Using High Power Battery Charger