an introducion of plecs

4/22/2013

1

electrical engineering software

An Introduction to

2

An Introduction to PLECS

Introducing Plexim

Key Features of PLECS

Modeling, Simulation and the Operation of PLECS

Thermal modeling

Special Features of PLECS

Solvers

Introducing PLEXIM

3 4

WHO IS PLEXIM?

Independent company

Spin-off from ETH Zurich

Privately owned by founders

Software PLECS sold since December 2002

Now in Release 3.2 September 2011

PLECS Blockset or PLECS Standalone

Customers in more than 40 countries

4/22/2013

2

5

Automation & Drives:Danfoss

Hilti

Rockwell

Woodward SEG

Electronics :Infineon

Panasonic

Philips

Tyco

SOME OF OUR CUSTOMERS TODAY

Aerospace: GoodrichSaabGE AviationUS Air Force

Automotive : Bosch

Chrysler

Opel

Skoda

High Power : ABB

Bombardier

GE Energy

Siemens

Academia : Aachen

Aalborg

Nottingham

Virginia Tech

Key Features of PLECS

6

KEY FEATURES OF PLECS

Fast and efficient simulation

Simple to use

Open component library

Accurate thermal modeling

The PLECS Scope

The two versions of PLECS:

PLECS Blockset

PLECS Standalone

Analysis tools

7 8

FAST AND EFFICIENT SIMULATION

Instantaneous switching

4/22/2013

3

9

SIMPLE TO USE

Drag and drop components

10

OPEN COMPONENT LIBRARY

Models are open for customization

11

THERMAL MODELING

Look-up table approach for speed

12

PLECS SCOPE

DTC_scope.plecs

CursorsRMS, Mean, Max, Min, Absolute MaxDelta,

THD, Fourier AnalysisX-Y plotExport to .bmp, .pdf, .csvCopy to Clipboard: Traces and Data

4/22/2013

4

13

PLECS SCOPE – Curve Tracer

X-Y Plot of Solar PanelPV_model_1.plecs

PV_model_2.plecs

Current characteristic of a single BP365 PV module.

Plot of 22 series-connected BP365 PV modules

14

PLECS BLOCKSET/STANDALONE

Available as Standalone or as a toolbox in Simulink

15

PLECS STANDALONE

An independent simulation tool.

Compatible with PLECS blockset

Key Features:

Control and circuit components

Faster simulation thanks to an optimized solver

Lower overall investment and maintenance cost

Faster than PLECS Blockset!

16

IMPORT FROM BLOCKSET INTO STANDALONE

Blockset Standalone

4/22/2013

5

17

IMPORT FROM BLOCKSET INTO STANDALONE

Blockset Standalone

18

EXPORT FROM BLOCKSET INTO STANDALONE

BlocksetStandalone

19

BLOCKSET AND STANDALONE MODEL COMPATIBILITY

MATLAB/Simulink

Standalone

PLECSControl blocksCircuit editor

Scope

PLECSSolver

Analysis tools and Script editor

PLECSControl blocksCircuit editor

Scope

Simulink Solver &Control blocks

Analysis tools and M/L Script editor

Blockset

Modeling, Simulation and the Operation of PLECS

20

4/22/2013

6

MODELING, SIMULATION AND THE OPERATION OF PLECS

Modeling, Simulation, Emulation

The Challenges and the Different Simulation Types

Ideal Switches

Basic Solver Types

Basic PLECS Operation

Behavioral Models in PLECS

21 22

FAILURE TO DO QUALIFIED SYSTEM MODELING ...

... results in tragedy

correct modeling

correct simulation

system

thermal

behavioral

(Thorough real-time controls testing (HIL))

23

MODELING VERSUS SIMULATION

ModelingFind essential functionality of target system

Describe components as simple as possible(model component details only as needed at this stage)

Enter the design using the modeling language

SimulationTransforming the model into mathematical equations

Solving the equations with specified tolerances

Providing numerical results

The accuracy of the simulation results depend on th e model

userP

LEC

S

24

CHALLENGES WITH NUMERICAL SIMULATION

Power semiconductors introduce extreme non-linearit yprogram must be able to handle switching

Time constants differ by several orders of magnitud ee.g. in electrical drives

small simulation time steps

long simulation times

Accurate models are not always availablee.g. semiconductor devices, magnetic components

behavioral models with sufficient accuracy are required

Controller modeled along with electrical circuite.g. digital control

mixed signal simulation

4/22/2013

7

25

DIFFERENT DEGREES OF SIMULATION DETAIL

Power circuit modeled as linear transfer functionsmall signal behavior

no switching, no harmonics

controller design

Power circuit modeled with ideal componentslarge signal behavior, voltage and current waveforms

overall system performance

circuit design and controller verification

Power circuit with manufacturer specific componentsparasitic effects (magnetic hysteresis)

switching transitions (diode reverse recovery)

component stress (electrical or thermal)

choice of componentsPower

converter

Controller

LoadPower input Power output

Controlsignals

Reference

Measurement

vi ii iovo

Heat

26

DIFFERENT DEGREES OF SIMULATION DETAIL

Controls

Circuit

Component

PLE

CS

Sta

ndal

one

Sab

er &

Spi

ce

Psi

m

Sim

plor

er

PLE

CS

Blo

ckse

t& S

imul

ink

27

HIGH SPEED SIMULATIONS WITH IDEAL SWITCHES

Conventional continuous diode modearbitrary static and dynamic characteristic

snubber often required

Ideal diode model in PLECSinstantaneous on/off characteristic

optional on-resistance and forward voltage

28

COMPARISON: DIODE RECTIFIER

Simulation with conventional and ideal switches

Simulation steps:1160 → 153

Computation time:0.6s → 0.08s

4/22/2013

8

29

STATE SPACE MODEL: BUCK CONVERTER

Switch conducting Diode conducting

30

OPERATING PRINCIPLE OF PLECS

Circuit transformed into state-variable system

One set of matrices per switch combination

31

VARIABLE VS FIXED TIME-STEP SIMULATION

Variable Time-Stephighest accuracy

time-step automatically adapted to time constants

can get slow for systems with many independently operating switches

Fixed Time-Stepcan speed up simulation for large systems

hardware controls are often implemented in fixed time-step

non-sampled switching events (diodes, thyristors) require special handling

32

VARIABLE TIME-STEP SIMULATION: BUCK CONVERTER

Transistor conducts

Diode blocks

4/22/2013

9

33


Transistor opens

Impulsive voltage across inductor

34


Impulsive voltage closes diode

35


36


Switch timing Problem:

diode opens too late

impulsive voltage across inductor

4/22/2013

10

37


35

Zero-crossing detection:

Time-step is reduced

Diode opens at the zero-crossing

38

HANDLING OF NON-SAMPLED SWITCHING EVENTS

Dio

de c

urre

nts

Dio

de v

olta

ge

Forward step

Non-sampledzero-crossing

Forward step


Backward interpolationDiode 3 starts conducting

Forward stepBackward interpolation,sync. with sample time


Forward stepBackward interpolation,Diode 2 stops conducting


Forward stepBackward interpolation,sync. with sample time

39

DIFFERENT DIODE MODELS IN PLECS

Diode turn-off

40

DYNAMIC DIODE MODEL WITH REVERSE RECOVERY

Reverse recovery effect under different blocking co nditions

4/22/2013

11

41

DYNAMIC IGBT MODEL WITH FINITE DI/DT DIFFERENT LEVELS OF SIMULATION

System simulationwaveforms resolved up to switching frequency

response times, controller behaviour

dead times, currents and voltages (peak, RMS etc)

harmonic content (Fourier, THD)

Thermal simulationefficiency, junction & heat-sink temperatures

semiconductor cooling, average and peak temperatures,temperature cycles, choice of devices, average power dissipation

Circuit simulation (single commutation cell)waveforms resolved to transient response

stray inductances and capacitances

common-mode currents

semiconductor tail-times, recovery times, spreading times.

42

3_L_3Ph_IGCT.plecs

Clamp_Rep_Real.plecs

Thermal Modeling

43

THERMA L SIMULATIONS

Semiconductor Losses

Ideal Switches vs “Continuous” Switches

Look-up Tables

Electrical-Thermal Simulation

Thermal Equivalent Networks

Steady-State Thermal Calculations

44

4/22/2013

12

45

SEMICONDUCTOR LOSSES

Switching Loss

Conduction Loss

Gate signal

46

SWITCHING LOSSES

Switching energy loss dependent on:

blocking voltage, device current, junction temperature, gate drive

EON = f(VCE, IC, TJ, RG)

Turn on Turn off

47

EXAMPLE IGCT TURN-OFF: VARYING STRAY INDUCTANCE

Courtesy ABB

0.0

1.5

3.0

4.5kV

0.0

1.0

2.0

3.0kA

VPK = 3800V

VDC = 2 kV

TJ = 125°C

5 10 15 µs

300 nH (10.5 Ws)

800 nH (12 Ws)

1500 nH (13.5 Ws)

tf ≈ 2.5µs, ttail ≈ 7µs

48

SWITCHING LOSS CALCULATION FROM TRANSIENTS

Accurate physical device models requiredgenerally unavailable

Physical parameters often unknown during design pha se.stray inductance of buss-bars

Small simulation steps requiredlarge computation times

4/22/2013

13

49

LOOKUP TABLE APPROACH FOR SWITCHING LOSSES

Instantaneous switching maintained for speed

Switching losses are read from a database after swi tching eventEsw = F(TJ, VBLOCK, ION) (RG = constant)

50

EXAMPLE LOOK-UP TABLE

Turn-off loss is a function of:

current before switching

voltage after switching

temperature at switching

RG is assumed constant

Exact loss found using interpolation

Note the voltage and current polarities!

Only data-sheet losses used in thermal calculations

Same procedure for EON, EREC and on-state

Report generation for reliable documentation5SNA 1500E330305_report.pdf

51

SEMICONDUCTOR CONDUCTION LOSSES

On-state loss

conduction profile is nonlinear:

vON = f(iON, TJ).

conduction profile stored in lookup table

exact voltage found using interpolation

conduction power loss:

PLOSS(t) = vON(t), iON(t)

Off-state lossnegligible - low leakage current

52

SIMULATION OF AN ELECTRICAL-THERMAL MODEL

4/22/2013

14

53

SEMICONDUCTOR THERMAL BEHAVIOR

54

OBTAINING SWITCHING LOSS DATA

Experimental measurements

switching losses highly dependent on gate drive circuit and stray parameters

use a switching loss setup to characterize loss dependency on voltage and current for two temperatures

Datasheets

given for a specific gate resistance and stray inductance

good approximations can be made by extrapolating manufacturers data (or asking for complete loss measurements)

55

POINTS TO NOTE

Thermal and electrical domains not coupled

Semiconductor losses from lookup tables don’t appear in the electrical circuit

Energy conservation may be achieved with extra feedback

The only ‘legal’ way is to use datasheet values !

Measurements only represent a few devices

Datasheets represent all devices over the lifetime of the component and over its production life

Transient simulations do not represent datasheet values

Only when you design your equipment using data-shee t values can you ask for help from your supplier ! Otherwise, if you are not respecting his data-sheet he won’t be willing to discuss your problem!

56

THERMAL DOMAIN

Thermal circuit analogous to electrical circuit

Thermal and electrical circuits solved simultaneous ly

4/22/2013

15

57

A COMPLETE ELECTRICAL-THERMAL MODEL

The heat-sink is the interface between the two doma insautomatically absorbs component losses

propagates temperature back to semiconductors

Thermal impedance modeled with RC elements

58

DIFFERENT THERMAL EQUIVALENT NETWORKS

Cauer equivalent

Physics based thermal equivalent circuit

Each Rth and Cth pair represents a physical layer in the thermal circuit

Foster equivalent

Curve fitting approach based on heating and cooling characteristics

No correspondence between Rth,n or Cth,n and the physical structure!

Any modification of the system requires recalculation of all values

59

MEASURING AVERAGE DEVICE LOSSES

ConceptCalculate total switching and conduction energy lost during a switching cycle

Output as an average power pulse during the next cycleImplementation:

based on a C-Script blockconduction and switching losses measured with a Probe

60

JUNCTION-CASE THERMAL IMPEDANCE

Define in semiconductor thermal description to obse rve junction temp fluctuations

Foster coefficients usually given in data-sheet

Example junction-case thermal impedance

Foster network coefficients

4/22/2013

16

61

FOSTER NETWORK PITFALLS

Only accurate if reference point x is a constant te mperature

Cannot be arbitrarily extended beyond point x

TJ is immediately affected by temperature changes at x

62

SOLUTION 1 - USE FIRST ORDER CAUER NETWORK

Calculate τ from 63% R value

C = τ/R

VC reaches 63.2% VFINAL after τ

63

COMBINED ELECTRICAL-THERMAL SIMULATION

Semiconductor losses don’t appear in electrical circuit

Conservation of energy can be maintained by subtracting thermal losses from electrical circuit

64

Calculate average device losses for each device

CYCLE-AVERAGE LOSSES

Average device losses

Average device losses

Apply to external resistive-only thermal circuit

4/22/2013

17

65

EXAMPLE IGBT CONDUCTION LOSSES

Instantaneous loss

Cycle average loss

Moving average (20ms)

66

CALCULATING THE STEADY-STATE OPERATING POINT

Challenge: Large thermal time-constant of heat-sink - simulation can take hours!

Newton-Raphson analysis

thermal capacitances left in circuit

Jacobian matrix must first be calculated

system must be periodic and all states must converge

Cycle-average losses with resistive thermal circuit

thermal capacitances are removed

losses are averaged, TJ = constant at steady-state

system can be non-periodic and have non-convergent states

Special Features of PLECS

67

THERMAL SIMULATIONS

Control Analysis Tools

Newton-Raphson Analysis

Magnetic Modeling

Custom Control Codes

Simulation Scripting

68

4/22/2013

18

69

ANALYSIS TOOLS

Control analysis tools

AC sweep

impulse response analysis

loop gain analysis

Steady-state analysis

BuckOpenLoop.plecs

NEWTON-RAPHSON ANALYSIS

Iterative method for finding the roots of an equation y = f(x):

If x is the initial state vector and

FT(x) is the final state vector after time T,

then to find the steady-state solution we must

find the roots of f(x) = x – FT(x)

This is done iteratively in PLECS by the Newton-Raphson method:

xk+1 = xk – J-1●f(xk) where J is the “Jacobian” (determinant) of the Jacobian matrix of the n state variables

(requires n+1 simulation runs)

70

NEWTON-RAPHSON ITERATION DEMO

71

NEWTON-RAPHSON ITERATION DEMO – GUESS X1

72

4/22/2013

19


73

NEWTON-RAPHSON ITERATION DEMO – TANGENT AT F(X1)

74

NEWTON-RAPHSON ITERATION DEMO – X2 FROM TANGENT

75


76

4/22/2013

20

NEWTON-RAPHSON ITERATION DEMO - SET X2 AS NEW ROOT

77


78


79


80

4/22/2013

21

NEWTON-RAPHSON ITERATION DEMO – SET X3 AS NEW ROOT

81

NEWTON-RAPHSON ITERATION DEMO - TANGENT AT F(X3)

82


83


84

4/22/2013

22

NEWTON-RAPHSON ITERATION DEMO – SET X4 AS NEW ROOT

85


86


87

NEWTON-RAPHSON ITERATION DEMO – CONVERGENCE!

88

4/22/2013

23

89

NEWTON RAPHSON: CONVERGENCE

Typically converges in less then 10 iterations

90

NEWTON RAPHSON: REQUIREMENTS FOR CONVERGENCE

The system must be convergent

ExampleProblem:PLL model

angle is a ramp signal towards infinity

Solution:create a periodic signal with a self-resetting integrator

2-level IGBT Inverter.plecs

91

MAGNETIC MODELING

Permeance-capacitance analogy

92

CUSTOM CONTROL CODE

Custom C-code

External DLL

4/22/2013

24

93

SIMULATION SCRIPTING

Inbuilt scripting

External scripting

BuckParamSweep.plecs

Solvers

94

95

OUTLINE

What are Solvers?

Discrete Solvers

trapezoidal rule

Continuous solversTaylor series polynomial

step-size control

acceptable error

tolerances: relative and absolute

refining the display output

Step-size selection for Discrete Solvers

Solver Comparisons

Conclusions

SOLVERS

In a digital simulation, integration is numerically performed by starting with known initial conditions

A time step is taken and some assumptions are made about the way a variable changes within this time step; the algorithm for do ing this is called a “Solver”

The simplest solver is one which assumes a linear c hange of conditions within a time step; this is a reasonable assumption for a sm all step. This type is known as a “Discrete Solver” and it builds the computed functi on from a series of trapezoidal blocks

96

4/22/2013

25

97

TRAPEZOIDAL RULE FOR DISCRETE SOLVER CONTINUOUS SOLVER

We will see later that discrete solvers have limita tions with regards to speed and accuracy.

A non-linear interpolation between two points might allow a larger time step, depending on how closely the interpolating function matches the real response.

Any waveform may be emulated by the sum of a suffic ient number of simple mathematical functions (e.g. by sine waves, in the case of Fourier).

Continuous Solvers, in fact, use the Taylor Series

98

99

TAYLOR SERIES EXPANSION

To perform a piece-wise simulation with a continuou s solver requires the approximation of a continuous function with a highe r order polynomial

The higher the order, the more accurate the solutio n

The Taylor series is of the form:

100

CONTINUOUS SOLVER OPERATION

If y(t) is the (unknown) function, it can be constructed in a piece-wise fashion from (known) points p1(t) and p2(t) from Taylor series polynomials.

A continuous solver determines the point yn+1 by calculating the equivalent Taylor series for p1(t).

An n th order solver has the same accuracy as an n th order Taylor series.

4/22/2013

26

REPRESENTATION OF EXPONENTIAL BY TAYLOR SERIES

Exponential

5th order Taylor series representation

At n = 8, “perfect” fit for -3 < x < 3

101

Source: Wikipedia

REPRESENTATION OF SINE-WAVE BY TAYLOR SERIES

102

1st order3rd order5th order7th order9th order11th order13th ordery = sin(x)

For -4 < x <4, a Taylor series to the 13th order is an accurate representation of y = sin(x)

Source: Wikipedia

103

CONTINUOUS SOLVER STEP-SIZE CONTROL

Step-size is automatically controlled by the solver (variable step) goal: keep the error within acceptable limits

advantages: accuracy directly specified by the user and fewer steps (faster simulation)

Step size, h, is calculated usingwhere:

ε is relative or “local” error

tolrel is relative tolerance

hold is previous time step

104

ACCEPTABLE ERROR

Local errordifference between 4th and 5th order solutions

Acceptable errordefines the local error limit

determined by tolrel except for small state values

Acceptable errorLocal error

Result is valid if:

4/22/2013

27

hold

STEP SIZE CONTROL

Step size automatically controlled by solver (variab le step) Goal: Keep error within acceptable error limits

Key advantage: Accuracy directly specified by the user

Step size calculated usingRelative error, ε (or “local error”)

Relative tolerance, tolrel

Previous time step, hold

105 106

TOLERANCES

Relative tolerance (tol rel) determines acceptable error limit when x approach es 0start with 10-3 (0.1%)

numerical limit is 10-16

Absolute tolerance (tol abs)best to set to “auto”

107

LC CIRCUIT - SCOPE OUTPUT

Display uses linear interpolation used between time-steps

Analytical solution:

Resonant LC circuit

VC(0) = 1 V

108

LC CIRCUIT - COMPARISON WITH ANALYTICAL SOLUTION

(tolrel = 1e-3)

Solver response

Analytical response

4/22/2013

28

109

LC CIRCUIT - SOLVER OUTPUT

Resonant LC circuit

VC(0) = 1 V

Calculated points for tolrel = 1e-3

110

OPTIONS FOR A FINER DISPLAY

Option 1: Reduce tol rel or time-stepsolver must recalculate polynomial coefficients at each time step

less efficient

Option 2: Increase refine factorsolver uses existing polynomial coefficients to calculate additional points.

more efficient

111

TRAPEZOIDAL RULE FOR DISCRETE SOLVER

112

FIXED SOLVER TIME-STEP SELECTION

Accuracy is indirectly determined by the time-stepto ensure accuracy, reduce the time-step and observe any changes in the output, or:

compare with a continuous simulation

Continuous waveformhighest transient frequency determines the sample time

set tsample < ttransient/10

for a ratio of 10, the integration error is approx -3% (underestimation)

Switched system switches must be turned on at sample instants

set tsample < tsw/100

4/22/2013

29

113

COMPARISON - CONTINUOUS AND DISCRETE SOLVERS

Simulated current

Time steps:

Continuous: tolrel = 10-6

Discrete: ts = 50µs

Underdamped RLC circuit

SUMMARY

Variable solvers are in general faster and more eff icientuse the Refine Factor for smoother displays rather than reducing tolrel or time-step

tolrel is typically set to 1e-3 to start with

tolabs is best set to auto

Fixed step solversdo not require tolerance inputs (set by step-size)

Refine Factor is always one (set by step-size)

114

Conclusions

115 116

CONCLUSIONS

Fast and efficient – ideal switches

Simple to use – Drag & Drop

Open component library customization of models

Thermal modeling – Look-up tables allow direct use o f semiconductor data-sheets

Magnetic modeling

Analysis tools – fast calculation of steady state an d frequency response

Custom control code – efficient controller design

Simulation scripting – fast performance analysis

PLECS Scope – high performance, user-friendly easy w aveform and data export

PLECS Blockset & PLECS Standalone – simple model exch ange (inter-company)

4/22/2013

30

117

electrical engineering software

Southeast-Asia Authorized Agents:Infomatic Pte. Ltd.Olivier WU 吳健銘

TEL: +65 3158 2943FAX: +65 3158 2190Mobile: +65 8478 0572Email: [email protected]: www.infomatic.com.sg

Vietnam Authorized Agents:Smart Green Solutions JSC27/35 Cong Hoa Street, Ward 4, District Tan BinhHo Chi Minh City, Vietnam.TEL: +84 8 38112941FAX: +84 8 38112941Email: [email protected]: www.sgs-jsc.com

an introducion of plecs

Documents

versions of plecs

plecs blocksetkey features

plecs standalonecustomers

simulation results

founderssoftware plecs

operation of plecsmodeling

efficient simulationsimple

script editorblocksetmodeling