modelling and control of ultracapacitor based …divsymposium/eecs2017/slides...modelling and...

Advisor: Prof. Vinod John

Modelling and Control of Ultracapacitor based Bidirectional DC-DC converter systemsPhD Scholar : Saichand K

Department of Electrical Engineering, Indian Institute of Science, Bangalore

Modelling and Control of Ultracapacitor basedBidirectional DC-DC converter systems

K. SaichandAdvisor: Prof. Vinod John

Power electronics group,Department of electrical engineering,

Indian Institute of Science (IISc), Bangalore - 560012.

Electrical Divisional Symposium

April 7-8, 20170 / 13

Comparison of energy storage elements

(a) (b)Source: https://upload.wikimedia.org/wikipedia/commons/6/6b/Supercapacitors_chart.svg

Advantages over batteries:Greater reliabilityUses non-corrosive electrolytes and low material toxicityHas higher power density, Low cost per cycleLow ESR => Fast charging and dischargingLow ESR => Low heating levels during charging and discharging

Disadvantages over batteries:Lower energy densityGreater self-discharge (Always needs a power conv. for regulating the voltage)High voltage dropLow ESR leads to rapid discharge when shorted

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https://upload.wikimedia.org/wikipedia/commons/6/6b/Supercapacitors_chart.svg

Comparison of energy storage elements

(a) (b)Source: https://upload.wikimedia.org/wikipedia/commons/6/6b/Supercapacitors_chart.svg

Advantages over batteries:Greater reliabilityUses non-corrosive electrolytes and low material toxicityHas higher power density, Low cost per cycleLow ESR => Fast charging and dischargingLow ESR => Low heating levels during charging and discharging

Disadvantages over batteries:Lower energy densityGreater self-discharge (Always needs a power conv. for regulating the voltage)High voltage dropLow ESR leads to rapid discharge when shorted 1 / 13

https://upload.wikimedia.org/wikipedia/commons/6/6b/Supercapacitors_chart.svg

Ultracapacitor based backup systems

Fuel cell/Batteries/

Other Energy sources

Critical Loads

Ultracapacitor bank charging

Bi-directional dc-dc converter Ride through provision

Ultracapacitor stack addresses:Short duration black-outsPeak power demandsLoad leveling the batterypacks in EV/HEV.

Ultracapacitors used widely inpower quality improvement,traction, EV/HEV etc;

2 / 13

Ultracapacitor based backup systems

Fuel cell/Batteries/

Other Energy sources

Critical Loads

Ultracapacitor bank discharging

Bi-directional dc-dc converter Ride through provision

Ultracapacitor stack addresses:Short duration black-outsPeak power demandsLoad leveling the batterypacks in EV/HEV.

Ultracapacitors used widely inpower quality improvement,traction, EV/HEV etc;

2 / 13

Power Supply for momentary power mains failures

UC

sta

ck +

_Critical Load

Two port network

SW3

UCs has a potential to replace batteries for light energy density applications.

UC based backup systems can be used in both grid connected or stand aloneapplications.

A non-isolated bidirectional converter is chosen since supply and UC stack sidevoltages are quite close.

System operates as buck converter during charging, boost converter duringdischarging.

During charging, UC stack voltage Vuc is regulated. During discharging,output voltage Vo is regulated.

3 / 13

List of contributions

1 PWM Blocking control for seamless mode transition

2 Virtual resistance control for seamless mode transition

3 Reduced order modelling of ultracapacitors

4 Generalized passives design for UC based backup system

5 Adaptive control during discharging mode of operation withenhanced performance

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List of works






3 / 13

PWM blocking for seamless mode transitionUC based converters have two operating modes - a) charging mode, b) dischargingmode.

Inner current loop

Charging mode

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Inner current loop

Discharging mode

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Inner current loop

Discharging mode

S3Charging DischargingS1

Both operating modes have similar control structuresbut different control objectives.

However, the two states share the same physicalelements of converter.

This necessitates a mode transition logic between controlmodes.

Smooth, seamless and fast transition between controlmodes is crucial.

4 / 13


Inner current loop

Discharging mode

S2

S3Charging Discharging

PWM Blocking

S1

or PWM blocking acts as a mode transition logic.

How long PWM blocking should be done?

This is decided by mode identification algorithm.

The proposed algorithm decides the control modesaccurately.

The algorithm is based on local parameters inductorcurrent, iL and output voltage, Vo.

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Mode identification algorithm

S2


PWM Blocking

S1

(1) (3)(2)

Starting

~~Charging mode Discharging mode

(4)

~~

~~

~~

~~

PWM Blocking

supply present supply absent

(a) (b)

or

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S2


PWM Blocking

S1

(1) (3)(2)

Starting


(4)

~~

~~

~~

~~

PWM Blocking


(a) (b)

or

Table: Logic conditions for mode identification.

Time durations iL Vo State

0<t<t1 iL<ITH Vo>Vb+∆V Charging mode (S1)

t1<t<t2 iL<ITH Vo<Vb−∆V Charging-Discharging tr. (S2)

t2<t<t3 iL>−ITH Vo<Vb−∆V Discharging mode (S3)

t3<t<t4 iL>ITH Vo>Vb+∆V Discharging-Charging tr. (S2)

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S2


PWM Blocking

S1

(1) (3)(2)

Starting


(4)

~~

~~

~~

~~

PWM Blocking


(a) (b)

or

Table: Logic conditions for mode identification.

Time durations iL Vo State

0<t<t1 iL<ITH Vo>Vb+∆V Charging mode (S1)

t1<t<t2 iL<ITH Vo<Vb−∆V Charging-Discharging tr. (S2)

t2<t<t3 iL>−ITH Vo<Vb−∆V Discharging mode (S3)

t3<t<t4 iL>ITH Vo>Vb+∆V Discharging-Charging tr. (S2)

Voltage and current hysteresisincluded.This reduces error modeidentification.

Fastest mode transition using

PWM blocking.

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Experimental results for PWM blocking

Smooth and seamless transition between control modes is achieved.

Accurate mode identification is performed using mode identification algorithm.

The proposed control allows decoupled controls for both operating modes.

During PWM blocking, no control on dynamics of inductor current iL.

A virtual resistance based control allows complete control over timeduration, inductor current iL dynamics during mode transition1.

1K. Saichand and V. John,“PWM block method for control of an ultracapacitor-based bidirectional

DC/DC backup system,” IEEE Transactions on Industry Applications, vol. 52, no. 5, pp. 4126-4134, Sept2016.

6 / 13

List of works






6 / 13

Reduced order modelling of ultracapacitors

UCs are usually modelled as series/parallel RC networks.Modelling of UC as a large capacitance in series with ESR is quite popular.Here, modelling of UC as a variable voltage source is studied.

(c) multi-branch model(a) series RC model (b) parallel branch model

(e) voltage source model(d) transmission-line model

+

_

+

_

+

_

+

_

+

_

+_

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Motivation for modelling of ultracapacitorsUltracapacitors as variable voltage sources

Table: Experimental set-up for UC based bidirectional dc-dc converter.

Hardware detailsFilter inductor, L 300µH

Filter capacitor, Cf 2000µF

UC stack†capacitance Cuc, ESR Ruc 12.5F , 0.2Ω

Maximum Power, Supply Voltage Vg , fsw 200W , 26V , 100kHz

† UC stack has 12 Maxwell BCAP0150 ultracapacitors in series.

ˆiL(s)

ˆd(s)=

sVgCuc

LCucs2 +R1Cucs+ 1=

Vg

Ls

s2 + R1Ls+ 1

LC

=

Vg

Ls

(s+ λ1)(s+ λ2)2

λ1 = −R1

2L−

1

2L

√CucR2

1 − 4L

Cuc≈ −666.268, λ2 = −

R1

2L+

1

2L

√CucR2

1 − 4L

Cuc≈ −0.4

Here, the approximation CucR21 L would be valid, allowing λ2 = 0, and λ1 = −R1

L.

(a) (b)In this work, it is shown UCs can be modelled as a 1st order system.

ˆiL(s)

ˆd(s)=

Vg

L(s+ λ1)(1)

2K. Saichand and V. John, “PWM block method for control of an ultracapacitor-based bidirectional








8 / 13








ˆiL(s)

ˆd(s)=

sVgCuc

LCucs2 +R1Cucs+ 1=

Vg

Ls

s2 + R1Ls+ 1

LC

=

Vg

Ls

(s+ λ1)(s+ λ2)2

λ1 = −R1

2L−

1

2L

√CucR2

1 − 4L

Cuc≈ −666.268, λ2 = −

R1

2L+

1

2L

√CucR2

1 − 4L

Cuc≈ −0.4


L.

(a) (b)

In this work, it is shown UCs can be modelled as a 1st order system.

ˆiL(s)

ˆd(s)=

Vg

L(s+ λ1)(1)









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ˆiL(s)

ˆd(s)=

sVgCuc

LCucs2 +R1Cucs+ 1=

Vg

Ls

s2 + R1Ls+ 1

LC

=

Vg

Ls

(s+ λ1)(s+ λ2)2

λ1 = −R1

2L−

1

2L

√CucR2

1 − 4L

Cuc≈ −666.268, λ2 = −

R1

2L+

1

2L

√CucR2

1 − 4L

Cuc≈ −0.4


L.

(a) (b)In this work, it is shown UCs can be modelled as a 1st order system.

ˆiL(s)

ˆd(s)=

Vg

L(s+ λ1)(1)









8 / 13

Comparison using z-domain bode plots

Why analysis in z-domain??The transfer functions of a buck converter feeding a UC stack, iL(z)

d(z)for both the

models are derived in z-domain.Usually, the control is implemented in digital platform.The non-idealities and other delays such as sampling and PWM delays can also bereadily incorporated in the z-domain models.

z-domain transfer functions obtained from continous time state space models.

Why use exact discretization?

The comparison ofˆiL(z)ˆd(z)

for both the models is performed for wide range of design

and operating conditions.

Discretization methods such as Forward and Backward Euler, Tustin’s method are

not accurate for wide range of sampling frequencies, fs3.

The comparison metrics are dependent on circuit parameters.

Po∈ (100W ,100kW ), Vg∈ (30V ,1000V )

3F.L. Lewis, Applied Optimal Control Estimation: Digital Design & Implementation, ser. Prentice

Hall and Texas Instruments digital signal processing series. Prentice-Hall, 1992.9 / 13

Comparison using z-domain bode plots

Why analysis in z-domain??The transfer functions of a buck converter feeding a UC stack, iL(z)

d(z)for both the

models are derived in z-domain.Usually, the control is implemented in digital platform.The non-idealities and other delays such as sampling and PWM delays can also bereadily incorporated in the z-domain models.

z-domain transfer functions obtained from continous time state space models.

Why use exact discretization?

The comparison ofˆiL(z)ˆd(z)

for both the models is performed for wide range of design

and operating conditions.

Discretization methods such as Forward and Backward Euler, Tustin’s method are

not accurate for wide range of sampling frequencies, fs3.

The comparison metrics are dependent on circuit parameters.

Po∈ (100W ,100kW ), Vg∈ (30V ,1000V )3F.L. Lewis, Applied Optimal Control Estimation: Digital Design & Implementation, ser. Prentice

Hall and Texas Instruments digital signal processing series. Prentice-Hall, 1992.9 / 13

Comparison ofˆiL(z)ˆd(z)

for the two UC models

−80

−40

0

40

80

120

160

200

Mag

nitu

de (

dB)

10−1

100

101

102

103

104

105

−270

−225

−180

−135

−90

−45

0

Pha

se (

deg)

Frequency (Hz)

Model−1Model−2Model−3

Model-2 and Model-3

Model-1

Figure: Bode plots comparing the three models forPo=200W , Vg=30V .

-50

0

50

100

Ma

gn

itu

de

(d

B)

101

102

103

104

105

-270

-225

-180

-135

-90

Ph

ase

(d

eg

)

Bode Diagram

Frequency (Hz)

Voltage source model

Series RC model

Deviation in two models

Ts = 10!5

Figure: Bode plots for current loop plant transferfunctions with PI control for Model 1 and Model 3.

Model 2 and Model 3 match closely which shows that λ2≈0 is a valid approximation.

For a given design application, Model 1 and Model 3 diverge especially at lowfrequency regions.The deviation between the two models reduces due to high gain of PI controller atlow frequencies.The high frequency characteristics determines the stability and bandwidth.

Phase margin of 70 and bandwidth of 10kHz is achieved.

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Comparison ofˆiL(z)ˆd(z)

for the two UC models

Charging mode inner current loop bandwidth, fb =4

2π∆tSettling time, ∆t of 70µs is observed based on which bandwidth of 9kHz is achieved.This verifies the dynamic performance of the designed inner loop current control.UC stack is charged in CC mode. The charging profile shows the stability of thedesigned current control.

The charging duration can be verified by Cuc∆Vuc

∆tc= iL.

The UC stack voltage, Vuc and charging current, iL is chosen to be low, so that

charging duration, ∆tc would be sufficiently high.

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List of works






10 / 13

Necessity and contributions

Generalized passives designWhy particularly necessary in UC based storage systems??

Batteries treated as fixed voltage sources.UC stack undergo greater depth of discharge.

Converter design should accommodate wide range of operating conditions.

Converter design should accommodate wide variation in UC stack voltage, Vuc.

The converter and passives’ design should also accommodate for both the chargingand discharging operating modes.

Generalized design of passives is necessary:

To validate any proposed ultracapacitor model,

For performance studies on a UC based dc/dc systems for wide range of designapplications.4.

Crucial in modeling of ultracapacitors and in design of adaptive control.

4K. Saichand and V. John, “A generalized design procedure for passives in a ultracapacitor based

bidirectional DC-DC system for backup power applications,” in Thirteenth Annual IEEE INDICON, 2016.IEEE Bangalore Section, 2016.

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List of works






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Adaptive control for discharging mode of operationUC stack

+

_

The control structure should accommodate for variation in:plant characteristicsRHP zero especially due to UC stack deep discharging.

Advantages of adaptive controlThe controller gains are estimated on-line.The proposed control ensures best performance criteria possible.

Adaptive control incorporates the variation of RHP zero and varies the bandwidth

accordingly5.

5K. Saichand and V. John, “Adaptive control strategy for ultracapacitor based bidirectional DC-DC

converters,” accepted for publication in Applied Power Electronics Conference. Tampa, Florida:APEC-2017, March 2017, pp. 1-6.

12 / 13

Conclusions and Contributions

Mode identification algorithm based on PWM blocking has been proposedwhich ensures:

Fastest mode transition.Smooth, seamless mode transition.

Accurate identification of control modes.

Alternately, virtual resistance control is proposed which allows control oncurrent dynamics during mode transition as well.

Simplified voltage source model for UCs similar to batteries have beenproposed and verified which simplifies the controller design.

The possibility of using this simplified model have been studied for wide rangeof design applications.

For this, a generalized passives design is carried out where the variation ofpassives for various design applications is carried out.

An adaptive control has been proposed which allows online variation ofcontroller gains to accommodate system characteristics and RHP zerovariation.

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List of Key Publications

[1] K. Saichand and V. John, “PWM block method for control of an ultracapacitor-based bidirectionalDC/DC backup system,” IEEE Transactions on Industry Applications, vol. 52, no. 5, pp. 4126–4134,Sept 2016.

[2] K. Saichand, A. Kumrawat, and V. John, “High performance AC-DC control power supply for low voltageride through inverters,” Sadhana, vol. 41, no. 2, pp. 147–159, 2016.

[3] K. Saichand and V. John, “Simplified modeling of ultracapacitors for bidirectional DC-DC converterapplications,” accepted for publication in Applied Power Electronics Conference. Tampa, Florida:APEC-2017, March 2017, pp. 1–6.

[4] K. Saichand and V. John, “Adaptive control strategy for ultracapacitor based bidirectional DC-DCconverters,” accepted for publication in Applied Power Electronics Conference. Tampa, Florida:APEC-2017, March 2017, pp. 1–6.

[5] K. Saichand and V. John, “A generalized design procedure for passives in a ultracapacitor basedbidirectional DC-DC system for backup power applications,” accepted for publication in ThirteenthAnnual IEEE INDICON, 2016. IISc Bangalore: IEEE Bangalore Section, December 2016, pp. 1–6.

[6] K. Saichand and V. John, “PWM block method for control of ultracapacitor based bidirectional dc/dcbackup system,” in 2014 IEEE International Conference on Power Electronics, Drives and EnergySystems (PEDES), IISc bangalore, December 2014, pp. 1–6.

[7] A. Kumrawat, K. Saichand, and V. John, “Design of AC-DC control power supply with wide input voltagevariation,” in 2013 IEEE Innovative Smart Grid Technologies-Asia (ISGT Asia), Nov 2013, pp. 1–6.

[8] K. Saichand, A. Kumrawat, and V. John, “Design of start-up power circuit for control power supplieswith wide input voltage variation,” in National power electronics conference. IIT Kanpur: NPEC,December 2013, pp. 1–6.

[9] K. Saichand and V. John, “Virtual resistance based control for ultracapacitor based bidirectional DC/DCbackup system,” in National power electronics conference. IIT Bombay: NPEC, December 2015, pp.1–6.

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Thank You....

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modelling and control of ultracapacitor based …divsymposium/eecs2017/slides...modelling and...

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