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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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