a generalised approach to pecs : principles to implementation · pdf filea generalised...

A Generalised Approach to PECs : Principles to

implementation

Mainak Sengupta

Dept. of EE,IIEST Shibpur,

Howrah, WB, India

December 22, 2015

(Dept. of EE, IIEST Shibpur, Howrah, WB, India)Generalised Approach to PECs 1/ 114 December 22, 2015 1 / 114

Presentation Outline

Presentation Outline

• Definition - What,Why, How - of PE

• Salient points from the definition

• Basics of PE Converters -How it works

• Pointers to a Generalised PE Converter!!!

• A 2X2 GPEC

• Simulation results

• Practical results

• Conclusions

• Acknowledgements

• References


Definition

Disclaimer with Apologies

This tutorial was planned by the speaker keeping in mind his troublesomedays in learning Power Electronics as a student. The obvious changes ofspace, time and perspective might have rendered those troubles in-existentto the present students. In that case the whole presentation has to beignored.All errors that exist in the presentation are the under the lone ownership ofthe speaker and any correct view, if at all present, are those of histeachers, the authors of the books he has read and of the students he hastaught over the past 18 years and 2 months.


Definition

Definition of PE- What?

Power Electronics (PE) is thattime branch of study within EE which dealswith analysis, design, synthesis, fabrication and operation of switchingcircuits (converters) for controlled conversion of electrical energy fromsome existing level and/or form (v1, i1, ac/dc) to electrical energy in someother desired level and/or form (v2, i2, ac/dc) using solid state (powerelectronic)devices. In the process the magnitude and direction of electricalpower (energy) flow can also be precisely controlled.


Definition

Definition - Why?

Electrical form of energy appears most user-friendly to human-society atpresent.


Definition

Definition - Why?

Controlled electrical energy to electrical energy transformations havebecome essential and unavoidable.


Definition

Definition - Why?

Say, a CRT based conventional desktop PC operating from 230V mains,for example, uses(5 different) voltage levels like 3V for the internal clock,15 kV for the CRT monitor etc.


Definition

Definition - Why?

Power Electronics technology (PET) - is the answer.


Definition

Definition - How?

Figure: Basic structure of a PE System


Salient points

Salient technical points

•The switching converter is at the heart of the entire PE system.

Figure: Equivalent configuration of a PEC


Salient points


•A switch is ideally loss-less in both the steady states.

ON-state:Psw−ON = vsw .isw = 0.i = 0 (1)

OFF-state:Psw−OFF = vsw .isw = v .0 = 0 (2)

• Practically, very small ON-state losses plus negligible OFF-state lossesadd up to steady-state losses totalling to about 0.5-1.5% of the netthroughput power.


Salient points


•Add switching losses!

Figure: Graphic representation of switching loss

Thus, net losses are typically 2 - 5 % of the throughput power.


Salient points


• A device having dissipation rating of say, 300 W can handle a power of10 kW

• Presently power handled by PECs in the entire range from mW to MW


Salient points


•So efficiencies in the range 95% - 98% are commonly achieved!

• Highest efficiencies achieved in resonant converters. Kept out of thescope of this discussion.

• Compare with efficiencies of linear electronic apparatus like voltageregulators which is around 45% typically.


Salient points


•Electrical dynamics take place in ms.

• N.B. - Switching dynamics have to be comparatively much faster, sayµs. Hence, solid state switching devices.


Salient points


• For switching of solid state two requirements are there:

Availability of appropriate devices with desired steady state characteristics-area under micro-electronics and material scienceAppropriate gate drive circuits- area under PE


Salient points


•Control of the converter is a must.


Salient points


•For closed-loop control - sensing, feedback and processing of appropriatesignals is a must.

Figure: Basic control structure in a PEC


Salient points


•Precisely controlled magnitude of electrical power may be made to flow ineither direction (load source !) giving smooth electrical energy transferand optimal performance in all 4-quadrants.


Salient points

An assurance

•All along we shall need very elementary laws namely, KCL and KVL onlyplus

• Very elementary mathematics.


Salient points

A reminder

Implications

KCL⇒ an existing current cannot be open-circuited and

KVL⇒ an existing voltage cannot be short-circuited.


Basic Principles

Basic Principles of the Rectifier

Rectifier Transformation: The concept

v1(t) = Vmaxsin(ωt)

= ImagVmaxej(ωt)


Basic Principles

Basic Principles of the Rectifier- contd.

Rectifier Transformation: The concept

v2(t) = q(t)v1(t)

= ImagKe−j(ωt+φ)Vmaxej(ωt)

= K1Vmax


Basic Principles

Basic Principles of the rectifier- contd.

Rectifier:

Figure: Input and desired output voltage waveforms for a 3-phase bridge rectifier


Basic Principles


Rectifier:

Figure: Typical circuit configuration of a 3-phase bridge rectifier


Basic Principles


Rectifier:

Figure: Graphical understanding of the rectification process


Basic Principles

Basic Principles of the Inverter

Inverter Transformation:The concept

v1(t) = Vdc


Basic Principles

Basic Principles of the Inverter- contd.

Inverter Transformation: The concept

v2(t) = q(t)v1(t)

= ImagKe j(ωt)Vdc

= KVdcsinωt


Basic Principles

Basic Principles of the inverter- contd.

Inverter:

Figure: Input and desired output voltage waveforms for a 3-phase inverter


Basic Principles


Inverter:

Figure: Typical circuit configuration of a 3-phase VSI


Basic Principles


Inverter:

Figure: Typical output voltage waveforms for a 3-phase VSI in 180o conductionmode


Basic Principles


Inverter:

Figure: Typical output voltage waveforms for a 3-phase VSI in 120o conductionmode


Basic Principles

Basic Principles of the inverter - contd.

Inverter:The Space Vector Concept

Vinv = vRn + avGn + a2vBn

where, a = 1∠120o


Basic Principles

Basic Principles of the inverter - contd.

Figure: Switching table in 120o and 180o conduction modes


Basic Principles

Basic Principles of the inverter-contd.

Figure: Space vectors associated with 3-phase Inverter


Basic Principles

Basic Principles of the DC-DC Converter

DC-DC Transformation: The concept

v1(t) = Vdc1


Basic Principles

Basic Principles of the DC-DC Converter- contd.

DC-DC Transformation: The concept

v2(t) = q(t)v1(t)

= KVdc1

= Vdc2

Vdc1Vdc1

= Vdc2


Basic Principles

Basic Principles of the DC-DC Converter- contd.

DC-DC Converter:Buck Converter

0 ≦ k ≦ 1

Boost Converter1 ≦ k ≦ ∞

Boost-Buck or buck-boost Converter

0 ≦ k ≦ ∞


Basic Principles

Basic Principles of the Frequency Converter

Frequency Transformation: The concept

v1(t) = Vmaxsin(ω1t)

= ImagVmaxej(ω1t)


Basic Principles

Basic Principles of the Frequency converter- contd.

Frequency Transformation: The concept

v2(t) = q(t)v1(t)

= ImagKe j(ω2−ω1)tVmaxej(ω1t)

= KVdcsin(ω2t)


Basic Principles

Basic Principles of the Frequency Converter-contd.

Figure: Block schematic of direct freq. conversion


Basic Principles

Basic Principles of the Frequency Converter- contd.

Figure: Block schematic of indirect freq. conversion


Possibilities of a generalisation

A Generalised Converter

Possible? - Perhaps!!!

Figure: Idea of a generalised PEC



Subsets of a Generalised Converter

Figure: Deriving a 3-phase bridge rectifier from a GPEC




Figure: Deriving a 3-phase inverter from a GPEC




Figure: Deriving a buck chopper from a GPEC




Figure: Deriving a boost chopper from a GPEC


GPEC Principles

GPEC - Motivation

• Search for an elementary unifying principle.

• Success of GTEM.

• Innocence about existence of such approaches in available textbooks.

• Forced exposure to handling CSI while attempting work on IH.


GPEC Principles

GPEC - Major clues

• A lecture by Prof. V. Ramanarayanan cited in the references of thislecture.

• The book by Prof. Philip T. Krein cited in the references of thislecture.


GPEC Principles

A 2X2 Switch Matrix

Figure: Generic representation of an ideal 2 X 2 PEC connecting a 2-terminalload with a 2-terminal source.


GPEC Principles

Source load dynamics

Input-output possibilities

• Voltage source connected to current sink/load.

• Current source connected to voltage sink/load.

• Voltage source connected to voltage sink/load.

• Current source connected to current sink/load.


GPEC Principles

Source load dynamics

Source issues:Voltage vs. Current source

Figure: Switch logic waveforms for V Source/C Sink


GPEC Principles

Switch configuration

Choice of switch configuration

Figure: Possible switching devices


GPEC Principles

The DC-DC Cases

DC V-Source, DC I-Sink

Figure: Voltage source feeding a current sink.


GPEC Principles

The DC-DC Cases


Switching Combination Result

q11, q12 vout = 0

q11, q22 vout = +vinq21, q12 vout = −vinq21, q22 vout = 0

Table: Switch Configurations for Converter associated with a voltage sourcefeeding a current load

N.B.: qij is the switching function of the switch connecting the i th rowwith the j th column of the switch matrix.

qij = 1, =⇒ SijON

= 0, =⇒ SijOFF


GPEC Principles

The DC-DC Cases


• To prevent KVL violation for V-source, no 2 switches of the samevertical should be ON together.

• To prevent KCL violation for I-sink, no 2 switches of the samehorizontal should be OFF together.

In mathematical shorthand,

q11 + q21 = 1 (3)

q12 + q22 = 1 (4)

• Interesting to plot qijs from the above!


GPEC Principles

DC-DC Cases

DC V-Source, DC I-Sink:Elements of 4-switch logic

Figure: Switch logic waveforms for V Source/C Sink


GPEC Principles

The DC-DC Cases


The output voltage equation(SOP)

vout = q11q12(0) + q11q22vin + q21q12(−vin) + q21q22(0)

= q11q22vin + (1− q11)(1− q22)(−vin)

= (q11 + q22 − 1) vin (5)

and, iin = (q11 + q22 − 1) iout , from power balance.

• Lot many implications reg. inst. waveforms, relative input-output

magnitudes etc.!


GPEC Principles

The DC-DC Cases

DC V-Source, DC I-SinkVo , the average output voltage (DC value, by definition), is of particularinterest.

Vo =1

T

∫ T

0voutdt

=1

T

∫ T

0(q11 + q22 − 1) vindt

= [1

T

∫ T

0(q11 + q22 − 1) dt]Vin

= (d11 + d22 − 1)Vin (6)

since duty ratios (d11 etc.,) are simply time average of the switchingfunctions.


GPEC Principles

DC-DC Cases

DC V-Source, DC I-Sink:4-switch logic for diagonal pairs

Figure: Switch logic waveforms for diagonal pairing


GPEC Principles

The DC-DC Cases


• Say, if the switches operate in diagonal pairs (maintaining (3),(4))=⇒ d11 = d22 = d . Then (6) reduces to,

Vo = (2d11 − 1)Vin (7)

• Interesting to plot Vo , putting different values of d11 in 87!

• Duty ratio in a DC-DC converter has the same effect as turns ratio ina transformer!!

• Different possibilities for 0.0 ≤ d ≤ 1.0 - negative or positive steadyaverage DC and something more (we shall see....VSI)!!!


GPEC Principles

The DC-DC Cases


• We recall

vout = (q11 + q22 − 1) vin

• We realise

the minus 1 term to be the culprit that causes negative average value for0.0 ≤ d < 0.5.

• We remove the culprit by setting q22 = 1 which =⇒ an always ONS22 or better a shorting link!!!!


GPEC Principles

The DC-DC Cases


• We redefine

vout = q11 vin (8)

• We redeem

Vo = d11 Vin

our familiar buck converter equation!!!!

• The rest of the circuit configuration naturally follows from (3).


GPEC Principles

The DC-DC Buck Converter

The familiar buck converter

Figure: The familiar Buck Converter derived from the Generalised Model


GPEC Principles


The familiar buck converter

(a) (b)

ioio

AA

BB

S1

S1

L1

D2 C1R

Vdc Vdc

vin D2 ioutvout

Figure: (a)Idealised uni-polar buck converter schematic and (b) Usual practicalrealisation.


GPEC Principles


The familiar buck converter: Selection of switching device S1

• The instantaneous voltage across S1 is,

vS1 = vin − vout

= (1 − q1)Vin

• while the instantaneous current through S1 is,

iS1 = iin

= q1Iout .

• Issue becomes clear if we can plot.


GPEC Principles


The familiar buck converter: Selection of diode D2

• Similarly, the instantaneous voltage across D2 is,

vD2 = vout

= q1Vin

• while the instantaneous current through D2 is,

iD2 = iin − iout

= (1 − q1)Iout .

• We can plot to understand better.


GPEC Principles


The familiar buck converter: Selection of L, C

−15

0

15

0.8

0.9

1

1.1

1.2

0 0.1 0.2 0.3 0.4

vL

(V)

i L(A

)

Time (msec)

Figure: Graphical explanation for choice of capacitor Farad-rating and inductorHenry-rating.


GPEC Principles


The familiar buck converter: Selection of L,C

iout = iL1 = Iout + ˜iout ,

= IR + iC1,

while, vout = ˜vout + Vout = vL1 + Vout ,

= vL1 + vC1.


GPEC Principles


The familiar buck converter: Numerical example

Vin (V) Vout (V) Pout (W) fs % vripple % iripple24 12 12 5k Hz ±5% ±5%

Table: Sample data


GPEC Principles


The familiar buck converter:: Number crunching

Iout =Pout

Vout

= 1.0A.

wherefrom we get,

Req =Vout

Iout= 12.0Ω.


GPEC Principles


The familiar buck converter:: Number crunching

∆iL1|ON = ∆iL1|ON = d1TS

(Vin − Vout)

L1= 0.1A

=⇒ L = 0.5× 200µ ×(24 − 12)

0.1= 12mH


GPEC Principles

The DC-DC Cases

DC I-Source, DC V-Sink

Figure: Current source feeding a voltage sink.


GPEC Principles

The DC-DC Cases


• This configuration is an exact dual of the previous (buck converter)case w.r.t. source-load configuration and dynamics.

• To prevent KCL violation for I-source, no 2 switches of the samevertical should be OFF together and so on.

Here, the mathematical shorthand,

q11 + q12 = 1

q21 + q22 = 1


GPEC Principles

The DC-DC Cases


Here, the input voltage equation(SOP)

vin = q11q12(0) + q11q22vout + q21q12(−vout) + q21q22(0)

= q11q22vout + (1− q11)(1 − q22)(−vout)

= (q11 + q22 − 1) vout

or better, = (1− (q12 + q21)) vout

and, iout = (q11 + q22 − 1) iin , from power balance.


GPEC Principles

The DC-DC Boost Converter

The familiar boost converter

Figure: The familiar Boost Converter derived from the Generalised Model(Dept. of EE, IIEST Shibpur, Howrah, WB, India)Generalised Approach to PECs 76/ 114 December 22, 2015 76 / 114

GPEC Principles

The DC-DC Boost-Buck Converter

DC I-Source, DC I-Sink

Sl. No. Switching Combination Result Remarks1 2 at a time q11, q12 Input-side open fault X (Disallowed)2 2 at a time q11, q21 Output-side open fault X3 2 at a time q21, q22 Input-side open fault X4 2 at a time q12, q22 Output-side open fault X5 2 at a time q11, q22 iout = iin, vout = vin

√

(Allowed)6 2 at a time q12, q21 iout = −iin, vout = −vin X (Not allowed!)7 3 at a time q11, q21, q22 Input and Output isolated and FW

√

8 3 at a time q11, q12, q22 Input and Output isolated and FW√

9 4 at a time q11, q12, q21, q22 Input and Output coupled but FW√

Table: Switch Configurations for Converter associated with a current sourcefeeding a current load


GPEC Principles



• Impossible to achieve in a single stage. Can be proved!


GPEC Principles

The DC-DC Buck-Boost Converter

DC C-Source, DC C-Sink

Figure: Current source feeding a current load


GPEC Principles



Figure: Boost-Buck Converter


GPEC Principles




GPEC Principles


DC V-Source, DC V-Sink

Figure: Voltage source feeding a voltage load


GPEC Principles



• Impossible to achieve in a single stage. Can be proved!


GPEC Principles



Figure: Buck-Boost Converter


GPEC Principles

The DC-AC Cases

DC V-Source, AC I-Sink

Figure: DC Voltage source feeding an AC current sink.


GPEC Principles

The DC-AC Cases

DC V-Source, AC I-Sink• Again, for the same source-load dynamics, we can repeat,

Switching Combination Result

q11, q12 vout = 0

q11, q22 vout = +vinq21, q12 vout = −vinq21, q22 vout = 0

Table: Switch Configurations for Voltage Source Feeding a Current sink


GPEC Principles

The DC-AC Cases

DC V-Source, AC I-Sink

• For this source-load dynamics, we recall that if the switches operate indiagonal pairs (maintaining (3),(4)) =⇒ d11 = d22 = d . Then (6)reduces to,

Vo = (2d11 − 1)Vin

• AC output =⇒ putting average value of Vo = 0.

• But this =⇒ d11 = d22 = d = 0.5!!!

• But current has to be =⇒ switch configuration to be appropriatelychosen.

• We end up discovering the familiar 1-phaseVSI


GPEC Principles

The DC-AC Voltage Source Inverter

1-phase VSI

S1

Q1D1

S4

Q4D4

AVinB

S3

Q3

S2

Q2

D3

D2

VAB

Iout

Cin

Figure: Circuit diagram of a continuous current/inductive load based single phaseinverter fed from an ideal dc voltage source.


GPEC Principles


1-phase VSI

Figure: vi , vo simulated waveforms(Vin = 24 V, fs = 5 kHz, R = 8Ω, L = 19mH and C = 62µF ).


GPEC Principles


1-phase VSI

Figure: Output voltage and Device voltage simulated waveforms.


GPEC Principles


1-phase VSI

Figure: Output current(upper) and device current(lower) simulated waveforms.


GPEC Principles

The DC-AC Cases: Inverters

DC I-Source, AC V-Sink

• We mean the 1-phase CSI.

• Source load dynamics-wise CSI configuration can be derived fromBoost converter-type approach, just as VSI has been derived frombuck-converter like approach.


GPEC Principles

The DC-AC Current Source Inverter

1-phase CSI

Figure: Circuit diagram of an IGBT - based CSI.


GPEC Principles


1-phase CSI

Figure: Output voltage(upper) and current(lower) waveforms.(Dept. of EE, IIEST Shibpur, Howrah, WB, India)Generalised Approach to PECs 94/ 114 December 22, 2015 94 / 114

GPEC Principles


1-phase CSI

Figure: Output(upper) and device(lower) voltage waveforms.(Dept. of EE, IIEST Shibpur, Howrah, WB, India)Generalised Approach to PECs 95/ 114 December 22, 2015 95 / 114

GPEC Principles

The AC-DC Cases: Rectifiers

AC V-Source, DC I-Sink

• We are talking ofbridge rectifiers bridge rectifiers.

• Interestingly, being discussed almost at the fag end.

• Worth trying in situ now, in light of all that we discussed so long.

• The output DC side (current continuous) has a lower average voltage.w.r.t to the AC-side half cycle average in keeping with Buck typesource-load dynamics.


GPEC Principles

The AC-DC Cases: Rectifiers


• This is the 1-phase version of the AFEC.

• The source side grid is made into an I-source by use of theAC/line-side reactor .

• The output DC side has a DC-link Capacitor (V-sink)!

• The output DC side has an over-charging tendency in keeping withBoost type source-load dynamics.


GPEC Principles

The AC-AC Cases: Cyclo/Matrix- converters

AC V-Source, AC I-Sink

• We note that the load side RMS voltage is lower in keeping with the”buck” configuration.

• Yet to be tried.


Implementation

An ideal switch!!

Practical realisation of an ideal switch

Figure: Practical realisation of ideal switch


Implementation

A 2X2 GPEC - SEQUEL Simulation

Figure: Circuit diagram in SEQUEL (bfore CSI logic was built-in)(Dept. of EE, IIEST Shibpur, Howrah, WB, India)Generalised Approach to PECs 100/ 114 December 22, 2015 100 / 114

Implementation

A 2X2 GPEC - SEQUEL Simulation

Figure: Circuit diagram in SEQUEL with CSI logic built-in


Practical Verification

A 2X2 GPEC - Experimental Set-up

Figure: Practical Circuit Diagram




Mode ofSwitches Requirements

Operation

Buck

S11 Pulsed- 5-0-5-0 at 5KHzS12 Open G-S shortedS21 Open G-S shortedS22 Shorted- +5-0V DC Supply

Boost

S11 Shorted- +5-0V DC SupplyS12 Pulsed- 5-0-5-0 at 5KHzS21 Open(G-S Shorted)S22 Shorted- +5-0V DC Supply

VSI

S11 Pulsed- 5-0-5-0 at 5KHzS12 Pulsed- 0-5-0-5 at 5KHzS21 Pulsed- 0-5-0-5 at 5KHzS22 Pulsed- 5-0-5-0 at 5KHz

Table: Switching Requirements for Different Modes of Operation




Figure: Control Circuit Diagram




Modes K1 K2 K3 K4

Buck Mode 0 1 0 0

Boost Mode 1 1 1 0

VSI Mode 0 0 1 1

Table: States of the Four Accessible Pins in the Control Panel



A 2X2 GPEC - Lab Prototype

Figure: Fabricated Set-up under operation



Experimental Results- Sample waveforms

1-phase VSI

Figure: Device logic waveforms.




1-phase VSI

Figure: vi , vo waveforms.




1-phase VSI

Figure: Output vi , vo ,io waveforms.


Conclusions

Conclusions

• The generalised approach may serve to reassure mediocre students ofPE, like this speaker.

• It might help the novice to get a unifying tone through the otherwisenumerous circuit configurations.

• It works accurately in both pen and paper type analysis andsimulations.

• It is possible to be implemented on experimental set-ups with verygood agreement w.r.t. to analytically calculated/simulated results.

• Finally, it might be worth being introduced at the front-end of basicPE courses.


Regards

Acknowledgements

• Late Prof. K. V. Ratnam- my M.Tech and Ph. D Supervisor and myGURU.

• Late Prof. A.K. Chattopadhyay - ”Oh Captain, my Captain!”

• Prof. V. Ramanarayanan - for inspiring me to think in this direction.

• Prof. Mahesh B. Patil- for his SEQUEL and for his indulgence towardsme.

• My teachers at IIT-Kgp particularly,Prof. T. K. Bhattacharya - my Ph.D co-Supervisor, Prof. S. Sengupta and Prof. S N Bhadra.

• My classroom teachers at the UG level, particularly Prof. Sujoy Basu,Prof. Kalyan K. Ray, Prof. Anjan Rakshit and Prof. Tapan K. Ghoshal.

• Late Prof. V.T. Ranganathan - for his love.


Regards

Acknowledgements

• Prof. Sujit K. Biswas - for his continued support since my UG days atJU.

• The organisers of NPEC-2015, particularly Prof. Kishore Chatterjee forthis scope provided and helping me to learn a little more in the process.

• My teachers at all levels.

• All students, particularly at the my PG & R level and colleaguesatIIEST, Shibpur.

• All researchcolleagues 6 of whom are presenting papers here, and criticalresearch supporters Mr. N. Datta and A. Ghosh at APE Lab, EE, IIEST,Shibpur.

• My family, particularly my wife, for the continued support!

•Most importantly - all of you in the audience- who tolerated this earlymorning torture session.


References

BIBILOGRAPHY

Philip T. Krein, Power Electronics,Jan./Feb. 1970.

Majilya Writwik, Bhattacharya Soumya Tirtha and Pathak SambhutiStudies on A Generalised Power Electronic Converter, B.Tech ProjectThesis, EE, IIEST, May, 2014.

Ramanarayanan V., Power electronics and AC drives, Lecture atDubas Engineering, June, 2007.

Patil Mahesh B., SEQUEL: A Circuit Simulation Software, Users’Manual, Short Term Course, IIT, Bombay, 2001.

Cyril W. Lander, Power Electronics, June, 1970.

N. Mohan, T.M. Undeland, W.P. Robbins, Power electronics:Converters, Applications, and Design, Wiley India Pvt. Ltd., 2007.

Kjeld Thorborg , Power Electronics, July, 1979.


Thanks

GRATITUDE FOR YOUR KIND ATTENTION


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