High Resolution Converter for Battery ImpedanceSpectroscopy

Shimul Kumar Dam, Vinod JohnDepartment of Electrical Engineering,Indian Institute of Science, Bangalore.

(email: shimul@ee.iisc.ernet.in, vjohn@ee.iisc.ernet.in)

Abstract—Monitoring the condition of battery is beneficial formany applications. Internal impedance of the battery can be usedto monitor battery health. The power converter for interfacing thebattery bank, can be used to measure battery impedance insteadof using any dedicated commercial equipment, thus reducingsystem cost significantly. However, the power converter has someadditional requirements in terms of control and power circuit,to be able to measure battery impedance. This work analyzesthe power circuit requirements and describes possible methodsto meet them. These additional measures are necessary whenpower level is medium or high. Advantages and disadvantagesof each method are discussed. Among the suggested methods,the in-built PLL of FPGA is used to enhance PWM resolutionalong with an interleaved converter circuit approach is used tosuccessfully measure battery impedance with a 3 kW converter.

Keywords—Battery converter, impedance spectroscopy, voltageresolution, health monitoring, hardware requirements, interleavedconverter.

I. INTRODUCTION

Battery based electrochemical energy storage system isintegral part of many renewable energy systems, back-uppower systems, electric vehicles and many such applications.A large part of the cost of each of these systems is the costof the batteries. Hence, batteries must be utilized to theirfull extent in order to make the whole system economicallyacceptable. Over-charging and over-discharging are the maincauses of rapid loss of battery life [1]. Improper charge anddischarge profile can also have detrimental effect on batterylife. So, state of charge (SOC) and state of health (SOH) ofthe battery, should be monitored continuously to avoid anyof the aforementioned situations. SOC is defined as the ratioof available charge in the battery and capacity of the battery.SOH is the ratio of the present capacity of the battery andthe initial capacity of the battery [2]. The internal impedanceof the battery has been used as a useful means of monitoringbattery health in literature [2]–[6]. The main drawback of thismethod is that it requires impedance measuring equipment thatis often expensive. However, use of such dedicated equipmentcan be avoided by using the power converter, used for charg-ing and discharging of battery, to measure impedance. Thisapproach has been implemented in literature [7]–[10] in the

This work is supported by the CPRI, Ministry of Power, Governmentof India, under a project titled ”Power conversion, control and protectiontechnologies for Microgrid.

978-1-4673-8888-7/16/$31.00 2016 IEEE

last few years. But these works do not address the additionalrequirements for impedance measurement. These requirementsbecome more critical when power level of converter goes up.In [11], the additional requirements of control structure hasbeen discussed. But, additional hardware requirements havenot been reported so far. This work explores the issue ofthe capability of power converter to produce small pertur-bation necessary for impedance measurement. It points outthe limitations caused by higher dc bus voltage and discussesthe possible ways to overcome these limitations. Two of thesuggested methods are chosen for implementation and bothapproaches are experimentally verified.

230 V50Hz

D1

D2

S1

230V/66V,3kVA

D3

D4

S3

S4

S5

S6D6

DC-DC CONVERTER

D5

To Load

Battery

Ibat Iind

L1 L2

S2

Cdc

Lgrid

AFEC

Fuse

C

Fig. 1. Grid connected hardware setup for charging and discharging a batterybank.

II. HARDWARE TOPOLOGY

The hardware setup used for charging and dischargingthe battery is shown in Fig. 1. The charging and dischargingof the battery is controlled by the dc-dc converter. Energyexchange with grid is achieved by an Active Front EndConverter(AFEC) at unity power factor. The converter is ratedfor 3 kW. It can charge or discharge a battery bank ratedup to 100 V. The dc bus voltage is maintained at 120 V.The dc-dc converter has the additional job of producing smallperturbation for impedance measurement. In this work, dc-dc converter works in current control mode during impedancemeasurement. A small amplitude sinusoid is added with thedc current reference of the current controller. This producesa small current perturbation in battery current. This current

perturbation results in a voltage perturbation in battery terminalvoltage. Both of these perturbation are measured and used forimpedance calculation. The frequency of the reference sinusoidis in the range of the desired frequencies for battery impedancemeasurement. The detailed control requirements for impedancespectroscopy are described in [11].

III. IMPEDANCE SPECTROSCOPY

Battery is a complex non-linear system whose dynamicsis governed by electrochemical, thermal and electromagneticequations [12]. Terminal voltage and load current of batterydo not exhibit linear relation between them. However, a smallcurrent perturbation can produce a small voltage perturbationabout an operating point and those two quantities have a linearrelation. Hence, under small signal assumption, battery can betreated as a linear system and impedance of the battery canbe measured. In impedance spectroscopy, impedance of thebattery is measured over a frequency range at suitable intervals.An equipment, capable of performing impedance spectroscopy,has to produce sufficiently small perturbation in voltage orcurrent and measure both current and voltage perturbations.The requirements for impedance measurement are-

1) Temperature change during measurement should benegligible.

2) State of charge(SOC) of the battery should not changesignificantly.

3) Impedance at lower frequency provides more infor-mation about SOC and SOH [11], [14]. So, lowestfrequency of impedance measurement should be lowenough so that variation of impedance with SOC, canbe measured and monitored. However, measurementat low frequency leads to longer measurement timewhich goes against the requirements 1 and 2. Hence,the lowest frequency of measurement should not betoo low to cause any significant system drift duringthe measurement time.

4) The controller to produce perturbation, should be asfast as possible. If the response of the controller isslow, transients during frequency change would takelonger time to decay, leading to longer measurementtime. In such case, it becomes difficult to meet thefirst two requirements.

5) To ensure the validity of linear system assumption,the amplitude of voltage perturbation should notexceed 10 mV/cell [2], [3], [7]. At high frequency,battery impedance is low and even 10 mV/cell candraw significant amount of current to aggravate theproblem of system drift during measurement. So,amplitude of voltage perturbation should be as smallas possible.

Application of dedicated commercial equipments that canmeasure impedance over a wide frequency range fulfillingall these requirements, is mainly restricted to research anddevelopment, owing to their high cost. On the other hand useof power converter for impedance measurement is a feasiblesolution for commercial use. The controller for controllingbattery charging and discharging is used for producing smallperturbation required for impedance measurement. In this caseall the requirements for impedance measurement demand a

power converter whose control structure has adequate band-width and should be capable of producing a perturbation indesired frequency range with negligible steady-state error [11].The converter should also have high output voltage resolution.It is shown, in the subsequent sections, that interleaved dc-dcconverter along with the in-built PLL of FPGA can be used tomeet this objective.

IV. POWER CONVERTER BASED IMPEDANCEMEASUREMENT

In order to perform impedance spectroscopy, the powerconverter must be capable of producing small amplitude outputvoltage perturbation of desired frequency in addition to adc output voltage. If the upper limit of desired frequencyrange, is comparable to switching frequency, then it is difficultto produce perturbation at that frequency. However, since,impedance at lower frequency contains more information, thehighest frequency of impedance measurement, lies at leastone order of magnitude below typical switching frequency.So, the perturbation at the highest frequency of the desiredfrequency range can be easily produced. Measurement atlowest frequency, should not cause any problem either, as longas system drift during measurement is kept small. Producinga small amplitude sinusoidal voltage at output can be chal-lenging. Ideally, power converter is capable of producing anyvoltage at its output within its output range. But, in digitalimplementation of the controller, duty ratio is not continuousbut quantized. So, output voltage of the converter has afinite resolution. This voltage resolution should be sufficientfor producing the desired small amplitude perturbation. Now,effect of quantization of duty on output voltage, in terms ofPWM resolution is analyzed below.

A. Duty Cycle Resolution

The dc-dc converter in Fig. 1, acts as a bi-directional buckconverter whose output voltage is given by-

Vo = DVdc (1)⇒4Vo = 4DVdc (2)

Here, ‘D’ is duty ratio and ‘Vdc’ is dc bus voltage. So,minimum change of output voltage, which represents theoutput voltage resolution is proportional to minimum changein duty as expressed in (2). Lets assume that the control isimplemented in a digital platform whose system frequency is‘fsys’ and the switching frequency is ‘fsw’. Number of systemclock cycles available in one switching time period is givenby-

n =fsysfsw

(3)

Hence, the carrier can be incremented ‘n’ times in one switch-ing cycle if the carrier is a saw-tooth waveform. If triangularcarrier is used carrier can be incremented only n/2 times ina switching cycle leading to less duty resolution. Hence, onlysaw-tooth carrier will be considered for following discussions.In that case, carrier signal can have only ‘n’ discrete values.Consequently duty ratio can have only ‘n’ discrete values. So,resolution of duty ratio is given by-

4D =1

n=

fswfsys

(4)

(a) (b) (c)

Fig. 2. Photographs of the hardware setup showing (a) IGBT modules with heat-sink and dc bus capacitor in the bidirectional converter (b) filter elements inthe dc-dc converter, (c) battery under test.

From (2), we can find the output voltage resolution,

4Vo =fswfsys

Vdc (5)

The digital platform used in this work, has a system frequencyof 20 MHz. The switching frequency is 20 kHz and the dc busvoltage is 120 V. Using (5), the output voltage resolution is120 mV.

B. Voltage Resolution Requirement

The battery system should also be analyzed to find outif this voltage resolution is sufficient to produce desiredperturbation. In this work, 12 V, 9 Ah VRLA batteries [15]have been used. Each battery voltage can go upto 14.4 Vduring charging. Since, the output voltage rating of the dc-dc converter is 100 V, at-most 7 batteries can be connectedin series. Each 12 V battery has 6 cells. So, the maximumamplitude of voltage perturbation can be 60 mV/battery toensure linearity. However, linearity is not the only decidingfactor. At 50 Hz, the impedance of one 12 V battery is 30mΩ [15]. Thus, 60 mV peak sinusoidal voltage will draw 2 Apeak sinusoidal current at 50 Hz. This amount of ac currentcan change the cell temperature and can cause cell degradation.Moreover, if the impedance spectroscopy is done on load, accurrent of this magnitude will distort the load current. So, theac current amplitude should be small compared to chargingcurrent of the battery. The C/10 rate of the battery is 900mA. So, it would be satisfactory if the amplitude of sinusoidalcurrent perturbation can be restricted to 100 mA. In that case,the amplitude of applied voltage perturbation should be (100mA * 30 mΩ)= 3 mV. For, seven batteries connected in series,the maximum amplitude of voltage perturbation can be 21mV. Hence, the converter has to apply a sinusoidal voltageof amplitude 21 mV at its output. Clearly, the output voltageresolution of a conventional PWM converter is not sufficientfor this task. Output voltage resolution of the converter needto be improved.

V. WAYS TO IMPROVE OUTPUT VOLTAGE RESOLUTION

The equation (5) serves as a guide to improve outputvoltage resolution. One or more of the following actions canimprove resolution: reduction of dc bus voltage, increase ofsystem clock frequency and reduction of switching frequency.Following approaches are studied to select the suitable ones.

A. Reduction of DC Bus Voltage

Dc bus voltage of the converter is a designed quantity andcan not be selected over a wide range. It depends on thebattery bank voltage as well as grid voltage and the powerlevel. As the power level goes up, dc bus voltage also goesup. Literature regarding use of power converter as impedancemeasuring equipment, have considered low dc bus voltage. In[9] the charger for only 12 V battery is used for impedancespectroscopy. Dc bus voltage is 14 V in [10], 7.5 V in [8]and 13.8 V in [7]. So, if the power level demands a higherdc bus voltage, other ways to improve resolution have to beemployed.

B. Increase of System Clock Frequency

System frequency of the digital platform can be increasedby using phase locked loop (PLL) or using a digital platformwith higher speed grade. FPGA based controller has beenused here since it is much faster than DSP based system.The FPGA has to increment the carrier variable between twoconsecutive clock edges(which can either be rising or falling).So, the minimum time period, in turns, maximum frequencyis dictated by that computation delay. It is found by timinganalysis of FPGA that maximum possible clock frequency toensure increment of carrier properly in FPGA is 293 MHz.The on-chip PLL is used to generate a clock of 260 MHz.With this clock the voltage resolution improves to 9.23 mV.This alone is still not sufficient for generating 21 mV peaksinusoidal signal as total number of steps in the sinusoid willbe less than 6, leading to distortion in the generated sinusoid.

C. Averaging of Duty Ratio Over Multiple Carrier Cycle

Averaging of two different duty ratios will give a inter-mediate duty ratio. Similarly averaging over multiple carriercycles can produce the desired output voltage. Averaging overthree cycles will improve the voltage resolution three times.But PWM delay will increase by three times reducing controlbandwidth considerably, thus increasing the settling time. Athigher power level achieving high control bandwidth is adifficult task since switching frequency is normally kept low.So, averaging over large number of carrier cycles can not beafforded.

D. Series Converter

The battery converter is connected in series with a auxiliaryconverter. The auxiliary converter has low dc bus and is usedfor producing small amplitude perturbation during impedancemeasurement. But, this converter needs isolated dc bus and theswitches has to carry rated current. Thus, this approach leadsto complexity as well as lower efficiency. The reliability ofthe overall system is affected by the reliability of the seriesconverter.

E. Multilevel Converter

Multilevel converter has higher voltage resolution com-pared to two level converter. This approach leads to complexpower circuit. Also, the battery bank voltage is generally abouta few hundred volts. At this voltage level, multilevel approachmay reduce converter efficiency due to the conduction dropsinvolving a larger number of semiconductor devices.

F. Reduction of Effective Switching Frequency

Switching frequency of the converter is decided based onswitching power loss and filter requirement. Higher switchingfrequency will result in lower filter requirements but it willincrease the minimum possible output voltage change orequivalently, reduce voltage resolution as shown in (5). So,lower switching frequency is desirable from point of view ofperforming impedance spectroscopy. If switching frequency isreduced by ‘n’ times, there will be ‘n’ times improvement involtage resolution causing increase of filter size. On the hand,it is possible to reduce switching frequency keeping the ripplefrequency same as before, by using ‘n’ leg interleaved con-verter with coupled output inductors. This approach requiresadditional power circuit hardware. But, at higher current andpower level, use of interleaved converter is justifiable. In thisapproach, although PWM delay increases by ‘n’ times, thevoltage resolution can be improved by a factor of ‘n2’ with‘n’ leg interleaved converter. The power circuit required forthis approach is shown in Fig. 3(a).

VI. VOLTAGE RESOLUTION IMPROVEMENT BYINTERLEAVED CONVERTER

Voltage resolution improvement is explained here with anexample of 3 leg interleaved converter. Fig. 3(a) shows thetopology of the converter. This converter also needs commonmode inductors between any two legs. The approach of usingintegrated common mode inductors is adopted for the filter[13]. Fig. 3(b) shows the simulated current waveforms indifferent legs for 120 V dc bus, 0.5 duty ratio and 10 Ω resistiveload. The individual leg currents i1, i2 and i3 add together toproduce current ripple of frequency thrice of the frequency ofeach leg current.

fsw(interleaved) =fsw3

(6)

So, the output ripple frequency can be kept same as before andswitching frequency can be reduced to one third of the previousfrequency. From (5), the voltage resolution will improve bythree times. The inductors connected to converter legs, aremutually coupled, as shown in Fig. 3(a), to restrict the flow ofcirculating current among the converter legs [13].

L

L

LC

VdcL1

i1

i2

i3

i

Vbat

M

MM

v1

v2

v3

(a)

(b)

Fig. 3. Interleaved converter: (a) topology, (b) simulated current waveforms.

Further improvement in voltage resolution is possible byaveraging of duty ratios of the three legs. All three inductorsconnected to the converter legs have same design, hencetheir inductance and resistance can be taken to be same foranalysis. Lets assume that each inductor has inductance ‘L’and resistance ‘r’ and mutual inductance between any twoinductors is ‘M’. Applying KVL and KCL in the Fig. 3(a),we get the following equations,

v1 − v0 = Ldi1dt−M

di2dt−M

di3dt

+ ri1 (7)

v2 − v0 = Ldi2dt−M

di1dt−M

di3dt

+ ri2 (8)

v3 − v0 = Ldi3dt−M

di1dt−M

di2dt

+ ri3 (9)

i = i1 + i2 + i3 (10)

Adding (7), (8), (9) and using (10), we get,

v1 + v2 + v3 − 3v0 = Ldi

dt− 2M

di

dt+ ri (11)

The duty ratio of the legs are ‘D1’, ‘D2’ and ‘D3’. So, averagevoltages applied to different legs are ‘D1Vdc’, ‘D2Vdc’. Theaverage output current is ‘I’ and the average voltage acrosscapacitor is ‘Vo’ which can be expressed as Vo = DeffVdc.Here, ‘Deff ’ is the effective duty ratio seen by the battery.Taking average of both sides of (11) over one switching cycle,

D1Vdc + D2Vdc + D3dc− 3DeffVdc = rI (12)

⇒ Deff =D1 + D2 + D3

3+

rI

3Vdc(13)

If D1 = D2 = D3 = D then,

Deff = D +rI

3Vdc(14)

Lets say that the improved duty resolution is ‘4D’ afterreducing the switching frequency. Then minimum possibleincrement in duty ratio is ‘4D’. If D1 = D + 4D andD2 = D3 = D, then change in output current will be verysmall and hence change in the last term of (13) will benegligible. In this case the effective duty ratio would be,

Deff = D +4D

3+

rI

3Vdc(15)

Comparing (14) and (15), we can find out that minimumpossible change in effective duty ratio is 4D/3. So theduty resolution is improved from ‘4D’ to ‘4D/3’. From(5), output voltage resolution also improves by a factor ofthree. So, overall, a factor of nine improvement in voltageresolution is achieved. In general, based on (6) and (15), a ‘n’leg interleaved converter can provide ‘n2’ times improvementin voltage resolution. After replacing the dc-dc converterwith the three leg interleaved converter, the output voltageresolution improves to (9.23 mV/9)=1.025 mV. This resolutionis considered sufficient to produce a sinusoidal voltage of peak21 mV with the ability to limit the current excitation duringimpedance spectroscopy to 100 mA.

In this strategy average voltage applied by one leg is morethan others. If this situation continues for long time, current inthat particular leg will become much more than other two legs.In order to avoid such a situation, duty ratio values are rotatedamong the legs so that one leg can not get more duty ratiocompared to others continuously. For example, if in a particularcarrier cycle duty ratios of legs 1, 2, 3 are (D +4D,D,D),then in the next cycle, duty ratios will be (D,D +4D,D).This ensures minimum circulating current in the legs of theinterleaved converter.

VII. EXPERIMENTAL RESULTS

The improvement of resolution can be seen by comparingFig. 4(a) and Fig. 4(b). To measure the output voltage res-olution, the converter was run in open loop with resistiveload and the duty was incremented by the smallest valuepossible. Change in output voltage in each step gives theresolution of output voltage. From Fig. 4(a),the output voltageresolution of the single leg dc-dc converter is 2.16V/240=9mVand from Fig. 4(b), the output voltage resolution of the three

(a)

(b)

Fig. 4. Minimum variation of output voltage of (a) single leg dc-dcconverter(scale=2V/div., sensor gain=240), (b) three leg interleaved con-verter(scale=1V/div., sensor gain=960)

leg interleaved converter is 1.08V/960=1.12mV. These valuesare very close to theoretically predicted values.

In the Fig. 5, channel 2 shows the current waveform duringimpedance spectroscopy. Current amplitude is kept constantat 100 mA and the frequency is being varied from 100 Hzto 100 mHz. Channel 1 shows the corresponding variation inthe terminal voltage. The impedance of the battery increasesas the frequency reduces. So, the amplitude of the voltageperturbation increases. Fig. 5 also shows the capability of theconverter to produce desired perturbation.

Impedance of a 12V, 9Ah lead acid battery was measuredby the developed setup in the frequency range 0.1 Hz to100 Hz at logarithmically spaced intervals. For comparisonpurpose, the impedance of the same battery was measuredby a commercially available impedance measuring equipmentSolartron CellTest System [16] under same battery condition.This comparison is shown in Fig. 6, which indicates thatit is possible to obtain a good match between the batteryimpedance measured by the converter and that from a ded-icated measurement system. The RMS error is 2.91% for realpart of impedance and 5.5% for imaginary part of impedance.These errors can be partially attributed to the repeatabilityconsiderations of test on electrochemical system. To the verifyrepeatability of impedance measurement, same battery wastested twice by Solartron system with 15 minute rest inbetween and the RMS errors between these two sets of datawere found to be 1.46% for real part and 3.85% for imaginary

Fig. 5. Voltage and current waveform during impedance spectroscopy.Channel 1: Voltage waveform[scale=5V/div, sensor gain=240], Channel 2:current waveform[scale=5V/div, sensor gain=83 V/A.]

part.

10−1 100 101 1020.020.030.040.050.060.070.080.090.10

frequency (Hz)

real

part

ofim

peda

nce

(Ω)

Data from proposed setupData from Solartron System

10−1 100 101 102

0.00-0.01-0.02-0.03-0.04-0.05-0.06-0.07-0.08-0.09-0.10

frequency (Hz)

Imag

inar

ypa

rtof

impe

danc

e(Ω

)

Data from proposed setupData from Solartron System

Fig. 6. Comparison of impedance measured by the proposed setup andSolartron CellTest System [16].

VIII. CONCLUSION

The power converter for charging and discharging a 3kW battery bank, has been used for performing impedancespectroscopy for the purpose of health monitoring of thebatteries. Thus, use of any expensive dedicated equipmentfor impedance measurement is eliminated. The requirementsfor performing impedance spectroscopy have been discussed.

The ability of power converter to meet those requirementsis explored. The effect of dc bus voltage on the ability togenerate small amplitude perturbation, has been analyzed anda relation between dc bus voltage and output voltage resolutionhas been derived. Different ways to improve output voltageresolution without changing the dc bus voltage, have beendescribed. Using on-chip PLL of the FPGA and implementinga three leg interleaved converter, the output voltage resolutionhas been improved from 120 mV to 1 mV for 120 V dc busvoltage. The current perturbation generated is small comparedto charging current to ensure that load current is not distorted.The voltage perturbation is well within the limit of linearity ofbattery model. The methods suggested for better output voltageresolution, are experimentally verified on a 12 V lead acidbattery. The procedure followed here for 120 V dc bus voltage,can be applied to higher dc bus voltage to get desired voltageresolution.

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