Dig Sim of Power Electronic Sys

8/14/2019 Dig Sim of Power Electronic Sys

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Digital Simulation of PowerDigital Simulation of Power

Electronic SystemsElectronic Systems By the end of the course, you are some one who canBy the end of the course, you are some one who can

confidently be a part ofconfidently be a part of

A research group, design & development group, prototypeA research group, design & development group, prototype

implementation/ testing group,implementation/ testing group,

Familiar with Modeling, implementing those models inFamiliar with Modeling, implementing those models in

Matlab/Simulink/Pspice.Matlab/Simulink/Pspice.

Models:Models:single phase/three phase controlled &uncontrolledsingle phase/three phase controlled &uncontrolled

rectifiers, choppers, inverters,filters,DC and AC motors,rectifiers, choppers, inverters,filters,DC and AC motors,controllers and complete systems.controllers and complete systems.

Familiar with case studies of DSP based controllers ofFamiliar with case studies of DSP based controllers of

induction motors and switched reluctance motorsinduction motors and switched reluctance motors


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Power electronics system:Power electronics system:

Block DiagramBlock Diagram


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Key Features of Converter CircuitsKey Features of Converter Circuits

The circuit topology changes as the switches openThe circuit topology changes as the switches open

and close as a function of time under the guidance ofand close as a function of time under the guidance of

the controllerthe controller


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SPICESPICE

Simulation Program with integratedSimulation Program with integrated

circuit emphasiscircuit emphasis


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Transient analysis calculates all node voltagesTransient analysis calculates all node voltages

and branch currents over a time interval, andand branch currents over a time interval, and

their instantaneous values are the outputs.their instantaneous values are the outputs.

Circuit behaviour in response to time varyingCircuit behaviour in response to time varying

sources(.TRAN)sources(.TRAN)

Dc and Fourier components of the transientDc and Fourier components of the transient

analysis results (.FOUR)analysis results (.FOUR)


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ISPICEISPICE

Interactive circuit simulation with graphic output.Types of Analysis :

Dc Analysis .DC

Dc sweep of an input voltage/current source,a model

parameter,or temperature over a range of values(.DC)Determination of the linearized model parameters of non linear

devices (.OP)

Dc operating point to obtain all node voltages. (.OP)

Small-signal transfer function with small-signal gain,inputresistance,output resistance(.TF)

Transient Analysis:

Used for circuits with time-variant sources (ac sources and

switched sources)


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AC AnalysisAC Analysis

Used for small signal analysis of circuits withUsed for small signal analysis of circuits with

sources of variable frequencies.sources of variable frequencies.

Calculates all node voltages and branch currentsCalculates all node voltages and branch currents

over a range of frequencies , and theirover a range of frequencies , and their

magnitudes and phase angles are the outputs.magnitudes and phase angles are the outputs.

Circuit response over a range of sourceCircuit response over a range of source

frequencies (.AC)frequencies (.AC)

Noise generation at an output node for everyNoise generation at an output node for every

fre uenc .NOISEfre uenc .NOISE


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Use of computer SimulationsUse of computer Simulations Used as teaching aid to understand concepts.Used as teaching aid to understand concepts. In research to analyze the behaviour of newIn research to analyze the behaviour of new

circuitscircuits In industry to shorten the design processIn industry to shorten the design process

especially to study the influence of a parameterespecially to study the influence of a parameteron the system behaviour through simulationon the system behaviour through simulation

than on a hardware bread board.than on a hardware bread board.


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Description and analysisDescription and analysis

of a circuit require the followingof a circuit require the following

specs:specs:Element valuesElement values

NodesNodes

Circuit elementsCircuit elements

Element modelsElement models

SourcesSources

Types of analysisTypes of analysis

Output variablesOutput variables

PSPICE output commandsPSPICE output commands

Format of circuit files,Format of output filesFormat of circuit files,Format of output files


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Element Values :Scale suffixes and unit suffixesElement Values :Scale suffixes and unit suffixes

F=1E-15F=1E-15 V=volt,A=amp,HZV=volt,A=amp,HZ

P=1E-12P=1E-12

N=1E-9N=1E-9U=1E-6U=1E-6

MIL=25.4E-6MIL=25.4E-6

M=1E-3M=1E-3

K=1E3K=1E3

MEG=1E6MEG=1E6

G=1E9G=1E9

T=1E12T=1E12


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Outcomes of the SimulationOutcomes of the Simulation

Calculate circuit waveformsCalculate circuit waveforms

Dynamic and steady state performances ofDynamic and steady state performances of

systems.systems.

Voltage and current ratings of various components.Voltage and current ratings of various components.

Power loss calculations leading to optimum thermalPower loss calculations leading to optimum thermal

designdesign


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Choices of Simulation Tools

Circuit oriented simulators User supplies the circuit topology and the component

values.

The simulator internally generates the circuitequations,which are transparent to the user.

The user may have the flexibility of selecting the details

of the component models depending on the simulator.

Controllers may be specified by means of a transferfunction or by models of components such as operational

amplifiers and comparators etc.,


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Simulation Tools

Equation Solvers

Describing the circuit and the controllers by means of

differential and algebraic equations.

The equations must be developed for all possible states inwhich the circuit may operate.

Describe the logic that determines the circuit state and the

corresponding set of differential equationsbased on circuit

conditions.

Solution of these algebraic/differential equations by means

of software packages specifically designed for this purpose

that provide a choice of integration routines,graphical

output and so on.


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Circuit Oriented Simulators

Sl.No Key Features Disadvantages

1. Initial set up time is small Little control over the

simulation process

2. Easy to make changes in circuit

topology and control

Can lead to long

simulation times.

3. Focus is on the circuit rather

than on the mathematics of the solution.

Can lead to oscillation

problems

4 Built in models for the components and

the controllers(analog and digital) are

usually available.

Steps to overcome these

difficulties are not

usually apparent andmay require trial and

error.

5. Possible to segment the overall system

into smaller modules/building

blocks,that can be tested individuallyand then brought together.


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Method of solving in Circuit solving programs

SPICE?EMTP

Linear differential equations:

Trapezoidal method of integration used in

SPICE and EMTP.

Non Linear differential equations :

Newton Raphson iterative procedure.


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Principles of Steady State (DC steady state)converter analysisPrinciples of Steady State (DC steady state)converter analysis


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Current waveforms of a switchCurrent waveforms of a switch

mode convertermode converter D=ton/Ts ;where Ts=1/fs;whereD=ton/Ts ;where Ts=1/fs;where

fs=switching freqfs=switching freq


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Representing the functions of a switching converterRepresenting the functions of a switching converter

by an equivalent circuitby an equivalent circuit

The dc transformer model:The dc transformer model:

Correctly represents the relationships between the dcCorrectly represents the relationships between the dc

voltages and currents.voltages and currents.

The model can be refined by including losses,such asThe model can be refined by including losses,such as

semiconductor forward voltage drops and on semiconductor forward voltage drops and on

resistances, inductor core and copper losses.resistances, inductor core and copper losses.

The resulting model can be directly solved ,to find v, i,The resulting model can be directly solved ,to find v, i,losses andlosses and in the actual non ideal converter.in the actual non ideal converter.


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EquationsEquations

V=M(D)*VgV=M(D)*Vg

M(D)=equilibrium conversion ratio;M(D)=equilibrium conversion ratio;

M(D)=D .. for buck converterM(D)=D .. for buck converter M(D)=1-D ..for boost converterM(D)=1-D ..for boost converter

Ig=M(D)* IIg=M(D)* I


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The DC transformer ModelThe DC transformer Model

There are three ports:There are three ports:

A power inputA power input

A power outputA power output

A control portA control port

These functions are ideally performed withThese functions are ideally performed with100%100% and hence,and hence,

Pin=PoutPin=Pout

Vg*Ig =V*IVg*Ig =V*I


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Circuit Model of a buck converterCircuit Model of a buck converter


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Ideal Dc Transformer ModelIdeal Dc Transformer Model

V=M(D) Vg ;V=M(D) Vg ;

Ig=M(D) I.Ig=M(D) I.


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a)Use of DC transformer model of switching converter(power source modeled by

thevenin equivalent)

b)Simplification by referring all elements to secondary side

Output voltage=M(D)V1 R/ (R+M2DR1)


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Modeling of Inductor copper loss via series resistor RModeling of Inductor copper loss via series resistor RLL

RL L


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Extension of dc transformer model to model other propertiesExtension of dc transformer model to model other properties

of the converter. Non idealities such as power loss,/converterof the converter. Non idealities such as power loss,/converter

dynamics can be modeled by adding inductors and capacitorsdynamics can be modeled by adding inductors and capacitors

to the equivalent circuit.to the equivalent circuit.


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'0 V

LVg IR D


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'

'

( )

0

C

V Vt D IR R

VI

R

i D

D


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DI

V/R

R

'0

VI

RD


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Circuit Model

+

_

+

-R

DI

RL

Vg

DV

+

-

V

I


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'0 V

LVg IR D

'0 / I V R

D '

VI

RD

This is the desired solution for the converter output voltage V.

'

2

1 1

1'

L

V

Vg DR

RD


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'

2

1 1

1'

L

V

Vg DR

RD

0LR '

1

D

LR

The first term is the ideal conversion ratio, with

The second term

Describes the effect of the inductor winding resistance

< the conversion ratio is equal to the ideal value'

1

D

However as LR is increased, in relation to The second term is reduced

in value, and VVg is reduced as well. At D=1, the converter =0

2

1

1'

LR

RD

2' RD

2' RD

Decreasing the . LR increasesV

Vg but results in large inductance


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Construction of equivalent circuit modelConstruction of equivalent circuit model

Obtained by refining the dc transformer model, toObtained by refining the dc transformer model, to

account for converter losses.account for converter losses.

This allows us to determine the converterThis allows us to determine the converter

voltages, currents,andvoltages, currents,and using techniques ofusing techniques of

circuit analysis.circuit analysis.


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Inclusion of Semiconductor conduction lossess in the

converter model

( )C

v Vt

R Ri

( ) L on L onL

t Vg i i Vg I I v R R R R

( )C

v Vt i I

R Ri

( ) L D L D L D D

t Vg i i v Vg I I V v V V R R R R


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Inductor voltage and capacitor current waveforms

for the converter

L onVg I I R R

VI

R

t

t

( )C

ti

( )L

tv

V

R

L D DVg I I V VR R sDT ' sD T


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LIR

The dc component of the inductor voltage is given by

By collecting terms and noting that D+D=1, we obtain

This equation describes the dc components of the voltages around a loop containing the

inductor , with loop current equal to the dc inductor current I.

+

- Vg

'D

D V ' DID R

'D V

onIDR

+

-

--- +-

I

' ' 0' L on DDVg I ID D I D V V R R D R

' 0 L on L DL D D Vg I I D Vg I I v V R R R R


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' 0C

V V D D I

R Ri

The dc component of the capacitor current is

Upon collecting terms,one obtains,

' 0V

D IR

RDI

V

V/R


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Circuits drawn together

LR

+

-

'D

D V' DD R

'D V

onDR

+

-

- - +-

I

gV RV

V/R


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AC Equivalent circuit modeling


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In this modeling , we ignore the switching ripple,model only the under lying ac variations in theconverter waveforms.

E.g., some ac variation is introduced into the converter

duty cycle d(t), such that

d(t)=D+ Dm Cosmt, where D and Dm are constants,|

Dm |< D and the modulation frequency m is muchsmaller than the converter switching frequencys=2fs.


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t

Gate

drive

t

Averaged

waveform,Ts with

ripple neglected

m s

mod.freq and its

harmonics

depending on d as

well as freq resp on

the conv.

Sw.freq and

its

sidebandsSw.harmonics


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Spectrum of the output voltage waveform v(t)

Switching freq components and its harmonics are small in

magnitude if the switching ripple is small.

The spectrum contains a low frequency component at the

modulation frequency

The magnitude and phase of this component depend not only

on the duty cycle variation, but also on the frequency

response of the converter.

If we neglect the switching ripple,then this low-frequency

component remains.

The objective of ac modeling is to predict this low frequency

component.

m


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The switching ripples in the inductor current and capacitorvoltage waveforms are removed by averaging over one

switching period.

Hence low frequency components of the inductor and capacitor

waveforms are modeled by equations of the form

(t)

(t)

x(t) ( ) int

s

s

s

C

C

s

d TCdt T

where denotes the average of x t over an erval of lengthT

vi

T

(t)

(t)s

s

L

L

d TLdt T

iv

1

x(t) ( )s

s

t

ts

Tx d

T T


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The above equations describe how the inducto currents andcapacitor voltages change when non zero average inductorvoltage and capacitor current are applied over a switching

period.

Note that the inductor volt-sec and capacitor charge balance,predict that the right hand sides of equations for the aboveare zero when the converter is in equilibrium.

To obtain a linear model that is easier to analyze we usuallyconstruct a small signal model that has been linearized about a

quiescent operating point,in which the harmonics of themodulation or excitation frequency are neglected.


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Linearization of the diode i-v

characteristic

,

( )

( )

v V

v t

i t

=

i I

=

v

2A

Q point

i(t)

v(t)

0.8v

,v V i I

= =

then the relationship between v and i

is approximately linear v

= rD i


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Small Signal eq ckt modeling of the

diode.

A nonlinear diode conducting current i

i

rD

+

v

-

Linearized small signal model

The conductance 1/rD represents the slope of the diode

characteristic evaluated at the

quiescent operating point.The small

signal model describes the behavior for

small variations around the q point.


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Basic AC Modeling Approach

( )( ) ( )

( ) ( )( )

L g

C

di tv t L v t

dt

dv t v t i t C

dt R

( )( ) ( )

( )( )( )

S

S

S

L

C

di tv t L v t Tdt

v tdv t Ti t C i t Tdt R

We replace vg(t) and v with their low

frequency averaged values Ts

And Ts


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( )( ) ( )

( )( )( )

S

S

L g

C

di tv t L v t

Tdt

v tdv t Ti t Cdt R

'1

=[ ( ) + ( ) ]S

S S S

t T

L LT T TS t

v t v d d t vg t d t v t T

replacing them with their low

freq averaged values

' 1 ( )d t d t

' 1 ( )d t d t where

the right hand side contains no switching harmonics, and models only the low

freq components of the inductor voltage waveform.


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Buck-Boost converter waveforms :inductor voltage and inductor current

Lv t

S

g Tv t

ST

v t

0

'+S SS

L gT TTv t d v t d v t

( )i t

(0)i

SdT ST

( )S

i dT( )Si T

t

Sg T

v

LST

v

L

t

tSdT

ST


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Averaging approximation:

In steady-state, the actual inductor current waveform i(t) is periodic with period equal to theswitching period TS i.e.,i(t+TS)=i(t).

During transients, there is a net change in i(t) over one switching period.

This net change in inductor current is correctly predicted by use of the average inductor

voltage.

This is true ,based on the inductor equation, dividing by L and integrating both sides

from

The left hand side of the above equation is the net change in inductor current over one

complete switching period.

The equation states that this change is exactly equal to the switching period TS multiplied

By the average slope

( )

( )L

di t

L v t dt

1

1( ) ( )

S S

S

t T t T

L

t t

S S L T

di v d L

i t T i t T v t L

to :St t T

S

L Tv t

L


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Use of average slope leads to correct prediction of the final value

Averaging the capacitor waveforms

Inserting this into we get

This is the basic averaged equation which describes dc and low frequency ac variations in the

capacitor voltage.

The Average Input Current

It was found necessary to model to write an additional equation that models the dc component of theconverter input current.This allowed the input port of the converter to be modeled by the dc

equivalent circuit.

Upon averaging over one switching period, one obtains,

( Si T

'( ) ( ) ( )

( ) ( ) ( )S S SS

T T T

C T

v t i t v t i t d t d t

R R

( )( ) S

S

c T

C T

v ti t Cd

dt '

( ) ( )( )S S

S

T T

T

d v t v t c d t i t

dt R

( ) during subinterval 1

= 0 during subinterval 2

Sg Ti t i t

SS

g TTi t d t i t


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Dig Sim of Power Electronic Sys