Digital Simulation of Power Digital Simulation of Power Electronic SystemsElectronic Systems

By the end of the course, you are some one who can By the end of the course, you are some one who can confidently be a part of confidently be a part of

A research group, design & development group, prototype A research group, design & development group, prototype implementation/ testing group,implementation/ testing group,

Familiar with Modeling, implementing those models in Familiar with Modeling, implementing those models in Matlab/Simulink/Pspice.Matlab/Simulink/Pspice.

Models:Models:single phase/three phase controlled &uncontrolled single 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 of Familiar with case studies of DSP based controllers of induction motors and switched reluctance motorsinduction motors and switched reluctance motors

Power electronics system:Power electronics system:Block DiagramBlock Diagram

Key Features of Converter CircuitsKey Features of Converter Circuits

The circuit topology changes as the switches open The circuit topology changes as the switches open and close as a function of time under the guidance of and close as a function of time under the guidance of the controllerthe controller

SPICESPICE

Simulation Program with integrated Simulation Program with integrated circuit emphasiscircuit emphasis

Transient analysis calculates all node voltages Transient analysis calculates all node voltages and branch currents over a time interval, and and 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 varying Circuit behaviour in response to time varying sources(.TRAN)sources(.TRAN)

Dc and Fourier components of the transient Dc and Fourier components of the transient analysis results (.FOUR)analysis results (.FOUR)

ISPICEISPICEInteractive 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,input resistance,output resistance(.TF)Transient Analysis:Used for circuits with time-variant sources (ac sources and switched sources)

AC AnalysisAC Analysis

Used for small signal analysis of circuits with Used for small signal analysis of circuits with sources of variable frequencies.sources of variable frequencies.

Calculates all node voltages and branch currents Calculates all node voltages and branch currents over a range of frequencies , and their over 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 source Circuit response over a range of source frequencies (.AC) frequencies (.AC)

Noise generation at an output node for every Noise generation at an output node for every frequency (.NOISE)frequency (.NOISE)

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 new In 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 parameter especially to study the influence of a parameter

on the system behaviour through simulation on the system behaviour through simulation than on a hardware bread board.than on a hardware bread board.

Description and analysisDescription and analysisof a circuit require the following of 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

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

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

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

N=1E-9N=1E-9

U=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

Outcomes of the SimulationOutcomes of the Simulation

Calculate circuit waveformsCalculate circuit waveforms Dynamic and steady state performances of Dynamic 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 thermal Power loss calculations leading to optimum thermal

designdesign

Choices of Simulation Tools

Circuit oriented simulators User supplies the circuit topology and the component

values. The simulator internally generates the circuit

equations,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 transfer

function or by models of components such as operational amplifiers and comparators etc.,

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 in

which 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.

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 and may require trial and error.

5. Possible to segment the overall system into smaller modules/building blocks,that can be tested individually and then brought together.

Equation Solvers

Sl.No Key Features Disadvantages

1. Give total contrl over the simulation process, including the integration method to be used,time step of simulation,etc.,

Long time is required for the initial set up of developing all possible combinations of diffferential /algebraic equations.

2. Smaller simulation time. Even minor changes in the circuit topology and control may require just as much effort as the initial set up.

3. Being general purpose tools, can be useful in applications other than power electronics simulation

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.

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

Current waveforms of a switch Current waveforms of a switch mode converter mode converter

D=ton/Ts ;where Ts=1/fs;where D=ton/Ts ;where Ts=1/fs;where

fs=switching freqfs=switching freq

Representing the functions of a switching converter Representing 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 dc Correctly represents the relationships between the dc voltages and currents.voltages and currents.

The model can be refined by including losses,such as The 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 and losses and ηη in the actual non ideal converter. in the actual non ideal converter.

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

The DC transformer ModelThe DC transformer Model

There are three ports:There are three ports: A power inputA power inputA power outputA power outputA control portA control port

These functions are ideally performed with These functions are ideally performed with 100%100%ηη and hence, and hence,

Pin=PoutPin=PoutVg*Ig =V*IVg*Ig =V*I

Circuit Model of a buck converterCircuit Model of a buck converter

Ideal Dc Transformer ModelIdeal Dc Transformer Model

V=M(D) Vg ;V=M(D) Vg ; Ig=M(D) I.Ig=M(D) I.

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)

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

RL L

Extension of dc transformer model to model other properties Extension of dc transformer model to model other properties of the converter. Non idealities such as power loss,/converter of the converter. Non idealities such as power loss,/converter dynamics can be modeled by adding inductors and capacitors dynamics can be modeled by adding inductors and capacitors

to the equivalent circuit.to the equivalent circuit.

'0 V

LVg IR D

+-+

_ Vg

RL

D’V

I

'0 V

LVg IR D

'

'

( )

0

C

V Vt D I

R R

VIR

i D

D

D’I

V/R

R

'0

VIRD

Circuit Model

+_

+-

R

D’I

RL

Vg

D’V

+

-

V

I

'0 V

LVg IR D

'0 /I V RD

'

VI

RD

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

'

2

1 1

1'L

V

Vg D RRD

'

2

1 1

1'L

V

Vg D RRD

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 V

Vg is reduced as well. At D=1, the converter η =0

2

1

1'LRRD

2' RD

2' RD

Decreasing the . LR increases V

Vg but results in large inductance

Construction of equivalent circuit modelConstruction of equivalent circuit model

Obtained by refining the dc transformer model, to Obtained by refining the dc transformer model, to account for converter losses.account for converter losses.

This allows us to determine the converter This allows us to determine the converter voltages, currents,and voltages, currents,and ηη using techniques of using techniques of circuit analysis.circuit analysis.

Inclusion of Semiconductor conduction lossess in the converter model

( )C

v Vt

R Ri

( )L on L onL

t Vg i i Vg I Iv R R R R

( )L D L DL D D

t Vg i i v Vg I Iv V VR R R R

( )C

v Vt i I

R Ri

Inductor voltage and capacitor current waveforms for the converter

L onVg I IR R

L D DVg I I VR R

VIR

t

t

( )Cti

( )Ltv

V

R

LIR

' 0L on L D D

D Vg I I D Vg I I VR R R R

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.

+

-I

Vg

'D

DV ' DID R

'D V

onIDR

+

-

+- + -- +-

I

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

( ) ' 0C

V Vt D D I

R Ri

The dc component of the capacitor current is

Upon collecting terms,one obtains,

' 0V

D IR

R

D’I++

_

V

V/R

+

-I

'D

DV ' DID R

'D V+

-

+- + -- +-++

_

V